investing money solutions

C h a p t e r 1 : F i n a n c i a l M a t h e m a t i c s ;

I n v e s t i n g M o n e y

Note: Answers obtained in these exercises may vary I the technology used.

I r - n s o n 1 1 S i m p l e I n t e r e s t , p a c j e 14

. ' : - 000 ; r is 3 .5% or 0 .035; t is 8

)0(1 + (0 .035K8) )

)0

e va lue is $38 4 0 0 . h i A- Pfi + rt)

300; r i s 1.25% or 0 ,0125 ' f is 4

)0(1 + ( 0 . 0 1 2 5 K 4 ) )

3 va lue is $10 500 . c)A = P(1 + f f )

F is $25 000 ; r is 0 .5% or 0 . 0 0 5 ' t is 2

•0(1 + (0.005K2)) 0

i va lue is $25 250 .

• -iOO; r i s 7 .4% or 0 ,074; f is 2 0 0(1 + (0 .074) (20) )

/ * 0

.-f va lue is $29 760 . 2.a)A = P+ Pn

'.'..11; P = $500(•

5 0 0 0 + ( 5 0 0 0 ) ( f ) ( 5 )

( ' ,00 = 25 OOOf

I :>.')•}

0.06 = f

6500 - 5000 + (5000)( r ) (5)

1 f /» ( i 2 * , 0 0 0 r

6

Ar. i . i t - , f r , t rate of 6 % wil l a l low C a m to reach his goa l

P IS $ 5 0 0 0 : f is 6 % or 0.06; t is 3

71 = 5000(1 + (0 .06K3) )

A = 5900

C a m wil l have $5900 .

3. a) A = P(1 + rt)

P i s $ 1 0 0 0 ; r i s 5 % o r 0 . 0 5 ; n s 5 .4 = 1000(1 + (0,05)(5)) A = 1250

T h e fu ture va lue is $1250 .

De te rm ine the interest ea rned .

1 2 5 0 ^ 1000 = 2 5 0

Rate of return = ^ 1000

Rate of return = 0.25

T h e rate of return is 2 5 %

b | A 71 - P ( 1 -rrl)

P i s $ 1 0 5 0 ; r i s 5 % or 0.05; f is 5

A = 1050(1 + (0.05)(5))

A = 1312.50

T h e fu ture va lue is $1312 .50 .

P i s $ 1 0 0 0 ; r i s 6 % o r 0 . 0 6 ; f is 5 4 = 1000(1 + ( 0 . 0 6 K 5 ) ) A = 1300

T h e fu tu re va lue is $ 1 3 0 0 ,

CA P(1 + rt)

"i.idOO; r i s 5 % or 0 ,05; f is 5 ^000 ( 1 + (0 ,05) (5) )

0

n- ' - i ' jh i re value . •* i • .Q IJ /- / ' ( I +rt)

r ' -00; r i s 5 % or 0 ,05; f is 6 ••.'•'0(1 + (0 .05K6) ) ru)0

' •«"!>re va lue < . o r m a

' n.h A y ie lds the greates t fu ture va lue ,

i e the in terest ea rned

1 3 1 2 . 5 0 ^ 1 0 0 0 = 312 ,50

Rate of return = 3 1 2 ^ 1000

Rate of r e t u m = 0 ,3125

T h e rate of re turn for op t ion A is 3 1 . 2 5 % .

rt)

$ 4 0 0 0 ; r i s 2 . 3 % or 0 .023 ; l i s 5 1000(1 + (0 ,023X5) ) 1460

. 5 years , the fu tu re va lue is $ 4 4 6 0

P is $ 4 0 0 0 ; f is 2 . 3 % or 0.023- f is 10

A = 4000 (1 + ( 0 . 0 2 3 ) ( 1 0 ) ) A = 4 9 2 0

A f te r 10 yea rs , the fu ture va lue is $ 4 9 2 0 ,

5.A = P(1 + rt)

Brad 's G I C : P is $ 1 5 000 ; r i s 3 . 2 % or 0 . 0 3 2 ' t is 6 / I' Of 10(1 + (0 .032) (6) ) ' ' ' ' 7 mm

I he r.itu.e va lue of Brad 's i nves tment is $17 880

C i . r i - . G IC ; P is $ 1 5 000 ; r is 3 .3% or 0 0 3 3 ' t is 5

15 0.30(1 + ( 0 , 0 3 3 ) ( 5 ) ) ^ ' 17 4 7 5

f f iC future va lue of Chr is 's i nves tment is $17 4 7 5

Brad 's i nves tment wi l l have a g rea te r fu ture va lue

at matur i ty . Invest ing the m o n e y for one more year

resul ts in more interest ea rned than does invest inq

the m o n e y at a 0,1 % h igher interest rate.

G.a}A = P + Prt

A $15 000 , F = $ 1 2 000 , f = 10

15 000 = 12 000 + ( l 2 0 0 0 ) ( r ) ( l 0 )

3000 = 120 OOOr

^ J 3 0 0 0 _ ^

120 000

0.025 = f

A n interest rate of 2 . 5 % is needed for the C S B to

g r o w to $ 1 5 000 in 10 years .

F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l 1-1

li) A / ' n 1 >h

l> $ 1 / i)U(l f ? ' . T . » 1% ' y>3% or 0 .035. f 1 0

4 ( ton, i t I " 0

A 10 3<}'i ! I,,, u i i u . r •^.i!u.- ',i 111.- t : S B w o u l d be $16 200 .

7. a l T h e y wil l be equa l , e .g . , T h e pr inc ipa l , in terest ra te ,

and t e r m are equa l . Both ea rn $300 in interest .

b | No . e .g . . W i t h s imp le in terest , t he re is no advan tage to

hav ing it pa id m o r e o f ten .

c ) e .g . . T h e y m a y need the in terest m o n e y to pay a

month ly bi l l .

A , r 1- fM'UO , , ' . % o r 0 . 0 5 ; f i s 5

n H, i .n i „ , • t ' ( l ' . , (5) )

'jV„ - . . v e s t m e n t A is $12 500 ,

a ' ' r . ' M . J u o . - , ( .4% or 0 ,014 ; f is 10

•)(10))

4 1 . 1 . ' . - '

f h s>ui, <4 : i v e s t m e n t B ! S $ 1 1 4 0 0 .

C our. . .% 1.9% o r 0 . 0 1 9 ; f is 7

))(7)) e ' ^ A vO

tu i . j r r H.uf i nves tmen t C i s $11 330 .

r) I ' , J . ih i.i«o . =' 0 5 % or 0 .0105 ; f is 8

r.' 5 . n o f . C • . ) 0 . . 0 5 ) ( 8 ) )

l i n ; f u t u n - v ' ^ . u . _ of i r . v e s t m e n t D i s $ 1 0 840 ,

f i..<r 'JU .^f'•' r Ht l ion ty va lue to least : Inves tment A,

|,M..r^t H • iwe -s tment C, Inves tmen t D.

b ) Mo M . the- . i i nount of in terest not ea rned in the last

1 s yc i . i r IS i n s i i l l . c k - n t to c h a n g e rank ings .

| , , v - J f i i - f I i l"JiO semi -annua l l y , so f = 5 1.5 or 3.5.

f , S . 1 T " J 0 0 . .% 3" / -or 0 .05; f is 3,5

4 , o O ( . 0 ^ ~ 031 (3 .5 ) )

A - /on I he t u i u i e <.aiue o l - w e s t m e n ^ A I • '1. i i 7f -0 ,

B. Inves tment is pa id annua l l y . St. I H . 2 or 8.

P i ' $ 1 0 0 0 0 ; r is 1.4%> or 0.0 U , i 3

4 . i f i iMM) f1 + ( 0 . 0 1 4 ) ( 8 ) )

/ t - i l 120 Tt ie future va lue of i nves tmen t B is $11 120,

Inves tment is paid quar ter ly , so f is 7 1.5 or 5,5,

P i s $10 0 0 0 ; r i s i r / o or 0 ,019 ; f is 5.5

4 = 10 000(1 + (0 ,019) (5 .5 ) )

^ = 11 045

T h e fu ture va lue of i nves tmen t C is $11 045 .

D. Inves tmen t is paid annua l l y , so f is 8 ^ 2 or 6.

P ib $10 0 0 0 ; r is 1.05% or 0 .0105 ; t is 6

A - 1 0 000(1 + (0 ,0105) (6 ) )

A " 1 0 630 The iu ture va lue of i nves tmen t D is $10 6 3 0 .

9. a ) / t - ^'(1

!)t;;,ir<^«' n . $ •(>«}<). / V. ^ or 0 .025 ; f is 0,5

A '.h(iO( 1 1 (() i f ' 3 ) i ( i '41

A «>43 i nves tmen t is $ 3 6 4 5 .

l akiV-J C ' ^ ' i ' = • ^ is 0.5

A ^ ' ' .^!.2 Of)

! h e hiiuiv valu.« .4 I o l o y . f . n v e s t m e n t is $ 3 5 5 2 . 5 0 .

Of>|,;itfii,n(> Iho (l ihr-ron'.f

:if,.13 53!)2 fT) 3 2 3 0

f j i " , i r r ( wil l h VJ'- i ' J . ' '<<>i«'5 t han La toya af ter

6 mon ths .

b ) D e s i r e e ; 3645 - 3600 = 45

Des i ree wi l l ea rn $45 in interest .

I . i t o f a : 3552 ,50 - 3500 = 52 .50

La toya wi l l ea rn $52 .50 in interest .

De te rm ine the d i f fe rence ;

5 2 , 5 0 - 4 5 = 7.50 La toya wi l l ea rn $7 ,50 more in in terest t han Des i ree . c ) D e s i r e e :

45 rate of re turn = ^

rate of return = 0 .0125 or 1.25%

L a t o f a :

52.50 rate of return = ^

rate of re turn = 0 .015 or 1.5%

La toya 's rate of r e t u m is h igher than Des i ree 's rate

of re turn ,

10 . A r . p f f

A is $ 1 3 000 ; P is $10 000 ; ris 6 . 5 % or 0 .065

15 000 - 10 000 + (10 000) (0 .065) ( f )

5 0 0 0 = 6 5 0 f

f = 7 . 6 9

It wi l l take S h a u n 8 years to ea rn e n o u g h m o n e y to

m a k e the d o w n paymen t .

11. a ) 7 \ = P(1 + rt)

A is $20 0 0 0 ; r is 3 . 2 % or 0 .032; t is 5

20 0 0 0 = P(1 + (0 .032) (5) )

20 000 = 1.16P

P = $17 241 .38

b) 7\ = P + Prt

A is $25 000 ; P i- % 1 / 24 i .3; r is 3 . 2 % or 0 .032

25 000 = 17 241 38 + (17 241 38) (0 .032) ( f )

7758 .62 = 551.72f

f = 14,06

It wi l l take abou t 14.1 years for the G IC to be

$ 2 5 000 .

1-2 C h a p t e r 1: F i n a n c i a l Ma themat ics : i n v e s t i n g Money

A is $9400; P is $4700; t is

I ne annua l in terest rate is 12,5%, I.-. >. + rt)

Pm $4700 ; r i s 12,5% or 0,125- f is 16 71 = 4700(1 +(0,125K16)) A = 1 4 1 0 0

T h e va lue o f t h e inves tment w o u l d be $14 100.

13. a) T h e s lope of tho g r a p h w o u l d inc rease if the

interest rate inc reased . For e x a m p l e , the inves tmen t

current ly earr n terest eve ry 3 years , so it has a

s lope of ^ . A s teeper g r a p h w i th a s lope of | w o u l d

m e a n the inves tment is ea rn ing $2 of in terest eve ry

3 years . Th is cou ld only h a p p e n if the interest rate inc reased ,

b | e.g. . Simi lar : T h e y have the s a m e intere-st rate T h e s i tuat ions are rep resen ted by a l inear re lat ion that s lopes upward to the r ight. The g raphs re late m o n e y to t ime The g raphs have the s a m e s lope. Di f ferent ; They have d i f ferent pr inc ipa ls . T h e interest g raph star ts at (0, 0) whi le the inves tment g raph star ts at (0, 3) . T h e inves tmen t g raph s h o w s the va lue o f t h e inves tment and the interest wh i le the interest g raph on ly s h o w s on ly the interest ,

14. The C S B G r a h a m buys in year 1 is inves ted for 5 years . The C S B he buys in yea r 2 is inves ted for 4 years , and so o n . The C S B he buys in year 5 wi l i be inves ted for 1 year. De te rm ine the year ly va lue o f t h e

S B then add the va lues together

• ' I I r. e>, . ; , . ; , ,

I ' f e e r

I c . f a l

Y'im_ ind V a l u e ($)

j f i / b

1 1 o f

I 1.32

! 1 9 0

3 3 7 0

f . M h a i i ' s ir.ve'4m*-nt wil l he wor th 35570 d f tc i 5 years 15 Caro le 's accoun t pays in terest da i ly so she wil l ea rn 86 days of in terest w h e n she w i thd raws her m o n e y Conver t 86 days to a f ract ion of a year-

86 = 0,235...

3 D 5 A = P{1 + rt)

P is $24 000 ; r is 5 ,2% or 0 .052- t is 0 2 3 5 ^ = 24 000(1 +(0.112X0,235,..)) ^ = 24 2 9 4 . 0 4 9 . . .

Caro le w i thd rew $24 294 .05 w h e n she c losed her sav ings accoun t .

L e s s o n 1 .2 : E x p l o r i n g C o m p o u n d i n t e r e s t p a g e 1 9

i • , • )

E v e : P is $3000: r is 4 % or 0.04- t is 5 71 •-- Zmm^ + (0.04)(5)) A = mm

• '• • '''-^ ' '(•-,<•-,. ( •-. .Oe • '.'.e"> .,(t f, I >l»ly f - • , | , i r , j l (...,.. -i i , H , , , ]

A = P(i +(0.04)(1)) • •'••''•'•=1' ''>"iiiU .. ., . I

• '• "• -v ' i!'!. e> I' - . r , I s . ., .. • • , tab le to o rgan ize the answers .

• 'ff-'V I t'nmApM ( I f " " j Yc-ar e i . e » i , 4 . i . . , < , 'AU'.-) .0

[ j _ _ _ T 3 ^

j ' ' .1 ;e, "

l 4 1 3 3 7 4 ^ 5 9 ^

11 VVP"..'

> '.i-l "O

.•'"'JO

3640 QR Lci i iy s i r i ves iment is wor th $3649.96 af ter 5 years Ca lcu la te the d i f fe rence in interest 3649 .96 ^ 3600 = 49 .96

Lar ry 's i nves tmen t ea rned $49.96 mo re in in terest than Eve 's because his inves tment ea rned interest on the pr inc ipal a n d on the accumu la ted interest .

= P(1 + rt)

e a y n t A : P is $6500; r is 5 . 1 % or 0.051 - f is 4 )500(1 + (0.051 K 4 ) ) '826,00

nves tmen t in accoun t A is wor th $ 7 8 2 6 00 af ter four years ,

OmTus^I ''^ "'^ °' ^ = P(1 +(0.048K1))

Ca lcu la te the interest 4 t imes, us ing the va lue of 4 as the n e w va lue of P for each new year Use a tab le to o rqan ize the answerc;

YoiJi _ P r i n c i p a l f $ |

_ » _ _ t350fj ( l i i

/ _ „ _ 0 3 1 2 Os)

_ _ j / 1 3 3 9H

'7 _ _ J n a i 3 3

i he inves tn fc i i l in docoun i b is wor th $ 7 8 4 0 77

af ter four years . S y d n e y shou ld choose accoun t B b e c a u s e it wi l l earn more interest.

3. a) e.g. , no it is not poss ib le to tell as the pnnc ipa ls , interest rates, a n d t imel ines all d i f fer b H = P ( 1 + r f )

I n v e s t m e n t A : initial P is $ 6 0 0 0 ; r is 1.2% or 0 .012 ; f is 1 (for 4 years) . 4 - P ( 1 < (0 .012) (1) )

0 0 1 2 00^

f 4 r , i h2 . ) ] ^

7 f s i0 .77

P r i n c i p a l ( $ 1 600CL00

OOTZOC)^

6 1 4 4 J 6 ~

6218 .60

0072 .00 6 1 4 4 8 6 ^

6293 .23

R e t u r n o n i n v e s t m e n t A - 6 2 9 3 2 j 6 0 0 0 = 293 .23

F o y n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n y a l 1-3

I n v e s t m e n t B ^ / ' . . ; . , - . ( H H . M S n - e c u m i

4 5,l)fifl(1 i n j 0 4 M ' 4 i

K.J,',i„"'n.nv.e,t,ur..t|> n/'.Cl ',f)lHI 14nu l„vestmcmt (4-n.lMH r. $ muO. . ,s f.%-.r 0 ue. / r. ! (foi I. y<vir4 / , /'(I . n) ubi{1))

-J. I) a} ID '.4.".

I Yea r P r i n c i p a l ($)

' 4(100 UO

I 0 1 ( in

I • ; . f- in4 40

\ i ' i ' V t . ' l f4 1 n n | i } n "

i if \" i S44'«iO !.'( uif.i (••->, ipv» ' . l iu i - i i l C

Y c a r ^ e n d V a l i j o d ) _

1440 no _

44n4 40 _ _ > A/U4 Of.

' , S ( ) 4 4 01

^ j ')-^0? 4(1

' 4 4 / 4 ua

n , , / 4 U 4 4 U i i U e , 7 ' ' e . 4

! -e 4 , r . tn< (|a, s5«%-l r e i n m e<' i i r /e ' . ' - i 'X ' i ' i

« . . s s c „ . 1 . 3 : C o m p o u n d I n t e r e s t : F u t u r e V a l u e ,

| -Mt |e 5fl

R o w :

1(2)

R o w 3: f =

1 = 0.341, 13.2

_ . , I = 3.3

3 5 R o w 4 : i = —

3oO I = 0.009,

3

' 12 I (365)

I = P(1 + , f

P = 520 ; f = 4 . 5 % c o m p o u n d e d month ly .

1 = 2 : ^ = 0.003 7 5 ; f = 8 y e a r s . n = 8 . 1 2 = 96

A = 520(1 + 0 . 0 0 3 7 5 ) *

4 = 7 4 4 . 8 2 9 . . . T h e fu ture va lue of the i nves tmen t is $744 .83 .

7 4 4 829 - 520 = 2 2 4 . 8 2 9 . . . T h e total in terest ea rned on the inves tment is $224 .83 .

b ) P = 1400 ; r = 8 . 6 % c o m p o u n d e d semi -annua l l y ,

j ^ M ¥ . = 0 043 ; f = 15 yea rs , n = 15 • 2 = 30 2

^ = 1400(1 + 0 . 0 4 3 ) ^ °

A - 4 9 5 0 593 .. T h e fu tu re va lue of the i nves tmen t is $4950 .59 .

4 9 5 0 593 - ^ 1 4 0 0 = 3 5 5 0 . 5 9 3 . . . T h e total in terest ea rned on the i nves tmen t is $3550 .59 .

By llu- till.; t'l /;•• sni- .evf .ifin-nl 'Aiil doub le in

10 nu VH.»-.

I •» 4('t.-nnin. > tht; .-ic teal 4ou ! ) ! i i i o t :me:

-fi,, p,it»to,.li - f f n u o ! h . - . i n ; » i o n n t e r e s t r a t e i s 6 . 8 % . Iht; .,orrip()ui.4in.| p.-oud i;. oiu.n.i', or o n c e per year .

r i i f ' tenn ( in v«v)f 4 ''• •"T.ntiwn |ip-fuh!i.-volu*-!' d.,Ml4-3''fH.T. or $14 0 0 0 . ! iv.Av\ III.: f>n;iiK.!.i! aj»o!.e;sii-)n on my ca lcu la tor :

Ihf. hn.ihliinj tin«; H' 34 yt: »% wh ich IS very

f j , , . . . ; !o 14. . I 'dS' i f - ' ) ! i<> -.U v'.virs.

Hv 4..- 'U! ..1 . . , the i nves tmen t wi l l doub le in

i. 1 V(>-»>-.

! , d.'i. 'O! ..^'h J ac tua l doub l i ng t ime :

. , r , . ! . S850. T h e annua l in terest rate is 9 . 2%.

f h e c o m p o u n d i n g p e n o d is month ly , or 12 t imes

per year .

The term (in years) is unknown.

T h e fu ture va lue is doub le $ 8 5 0 . or $ 1 7 0 0 .

I used the f inanc ia l app l i ca t ion o n my ca lcu la tor :

T h e doub l ing t ime is 7 56 yea rs , w h i c h is very d o s e to the es t ima te of 7,83 years .

c l ' ' ' ' ' o15 . . . ' 15,6

Us ing the rule of 7 2 , it t akes 4 .62 yea rs for the

i nves tmen t to doub le in va lue .

T h e pnneipa l is 3 1 / 300 . T h e annua l in terest rate is 15 .6%. T h e c o m p o u n d i n g penod is week l y , or 52 t imes per

year . The term (in years) is unknown. T h e fu tu re va lue is doub le $12 500 , or $25 000 .

1 used the f inanc ia l app l i ca t ion on my calcu lator ;

T h e doub l ing t ime is 4 .45 yea rs , w h i c h is very

c lose to t he es t ima te of 4 .62 yea rs .

d) 1 1 = 26.666. . .

Us ing the rule of 7 2 , it t akes 26 .67 yea rs for the

i nves tmen t to doub le in va lue .

T h e pnneipa l is $40 0 0 0 . T h e annua l in terest rate is 2 . 7%. T h e c o m p o u n d i n g per iod is sem i -annua l , or

2 t imes per year .

The term (in years) Is unknown.

T h e fu ture va lue is doub le $40 0 0 0 , or $80 000 .

I used the f inaneia l app l i ca t ion on my calculator :

T h e doub l ing t ime is 25 .85 yea rs , wh i ch is c lose to

the es t imate of 26 .67 yea rs .

1.4

i i | a ) T h e pr inc ipa l is $ 7 0 0 0 T h e annua l in terest rate is 6 J %

s 38, T h e c o m p o u n d i n g per iod is a n n u a l , or o n c e per year . T h e te rm (in years ) is 35 ,

The future value is unknown. A = P(1 + / ) "

A = 7000 (1 + QMm'f

A B9 9 9 9 , 0 0 7 , , ,

T h e fu tu re va lue of the i nves tmen t is $69 999 0 1 .

69 9 9 9 . 0 0 7 . . . ^ 7000 = 62 9 9 9 . 0 0 7 . . .

T h e total interest e a r n e d is $62 9 9 9 . 0 1 .

b ) T h e pnne ipa l is $ 8 5 0 . T h e annua l in terest rate is 9 . 2 %

so / = 0 092 . T h e e o m p o u n d i n g per iod is month ly . T h e

t e r m (in yea rs ) is 20 ,

n = 20 • 12 = 2 4 0

The future value is unknown

A = P(1 + if

A = 850(1 + 0,092f^ '^

A = 5 3 1 4 . 6 3 0 . . .

T h e fu tu re va lue of the i nves tmen t is $ 5 3 1 4 , 6 3 .

5 3 1 4 . 6 3 0 . . . - 8 5 0 = 4 4 6 4 . 6 3 0 . . .

T h e total in terest ea rned is $4464 63 .

c ) T h e pnneipa l is $12 500 .

T h e annua l in terest rate is 1 5 . 6 % so i = 0 156.

T h e c o m p o u n d i n g penod is week l y , or 52 t imes per year .

Xhrt t ^ rn - " e a r s ) is 5.

0

le is unknown.

• ih.( 0.156)-260

1 h' : A-j-K .'.'i.je of the i nves tmen t is $ 2 7 236 .58 ,

2 / ' 4 3 3 3 - 1 t 500 = 14 736 .58

I h c S4c4 ,n4 . . iSt ea rned is $14 736 .58 . 41 inr< pr ; i i ,o(. il is $40 000 .

i ne annua l interest rate is 2 . 7 % so i = 0 .027

T h e c o m p o u n d i n g per iod is sem i -annua l , o r 2 t imes per year

T h e te rm (in yea rs ) is 8.

n = 8 • 2 = 16

The future value is unknown.

A = P(1 4 if

A = 40 000 (1 + 0 . 0 2 7 ) '

A = 49 572 .410 . ..

T h e fu ture va lue of the i nves tmen t is $49 572 .41

4 9 572 .41 - 4 0 000 = 9572 .41

T h e total interest ea rned is $ 9 5 7 2 . 4 1 .

4. a)

46

Pr inc ipa l ($) 3 0 0 0 " o o o t ) ~ In terest Ra te per A n n u m ^0.09 ^ 0 .09 P e r i o d s per Year f 1 2 V a l u e at E n d o f Y e a r

o" 3000 ou " " 3000 00

3885 .09 3925 93

H 6 .3031.30 3 1 3 / . 6 6 9 6515 .68 6723 .37

12^ 8 4 3 7 . 9 9 8 7 9 8 51 13 10 927 .45 " ' 11 5 i 4 " r < 18 14 151.36 1 13 067 91 J

T h e cur rent va lue of the inves tment w i th interest i.r!'|. n,.irfihl-/ I , S I S Of,..- •! i

! ) ! ' . i!- , i ' !l.f. ri«( 1

Vf .11 . A n i m a l M o n t h l y

e o t i j i j o i i r i c i i s i g • . o o i p f . o n d m c }

n ca.n 4 < / '

,•() I 'M) • "

f.3

••4:i> 3 0 j J ^

\ 7 o , - / 4 s I

l l : 3 ' ih '•

{) n v h 3M

^ i 3 . ' ' 0 4

j f / , '/

n/4 , ' . i f .

; ; n 4 i lT.

1 0 3 / o» f

12 00C

I- i-f -

? < »s: .

' •')'.'i

< >••• > ]

c

• monthly compounding

• annual

c ) A s c o m p o u n d i n g f requency inc reases , interest rate g rowth inc reases .

Us ing the rule of 72 . it wil l take 15 years for Parker to doub le his inves tment .

Us ing a f inanc ia l app l ica t ion :

T h e pnneipa l is $6000 .

T h e annua l interest rate is 4 . 8 % .

T h e c o m p o u n d i n g per iod is annua l , or once per year.


T h e fu ture va lue is doub le $ 6 0 0 0 . or $12 000

T h e doub l ing t ime is 14,78 years , wh i ch is c lose to the es t imate of 15 years .

15 - 10 = 5

Us ing the rule of 72 , Parker wou ld be ab le to buy

his moto rcyc le 5 years sooner .

Us ing a f inanc ia l app l i ca t ion :


T h e annua l in terest rate is 7 .2%.

T h e c o m p o u n d i n g penod is annua l , or once per year.


T h e fu ture va lue is doub le $ 6 0 0 0 , or $12 000 .

T h e doub l ing t ime is 9.97 years , wh ieh is c lose to

the es t imate of 10 years .

14.78 - 9.97 = 4.81

Parker w o u l d be ab le to buy his moto rcyc le 4 .81 years sooner .

T h e cur ren t va lue of the i nves tmen t w i th in terest

c o m p o u n d e d annua l l y is $14 151.36 .

F o u n d a t i o n s of M a t h e m a t i c s 12 S o l u t i o n s Manual 1-5

6. T h e pr inc ipal is $250 000 .

T h e annua l interest rate is 3 .8%.

T h e c o m p o u n d i n g per iod is s e m i - a n n u a l , or 2 t imes per

year . T h e te rm (in years ) is 1 .

r? = 1 • 2 = 2


/ I = P(1 + if

A - 230 onn(i I 0 033)- '

A - e s n nou oof! 1 IIP volur .)? Ih<- hu-st mod a f ter one year is $ 2 5 9 690 .25 ,

' n o t j o o . " , 0 f.9(i'OS 0 5 9 0 . 2 5

ii„- Pu'.l tinid l'.:c. 39')',in 25 ava i lab le e a c h year .

Bool? A IS- o''.-- 'on! !S $20 0 0 0 , I ht .in.0.4 in>--i' '.I oti? I ; 6 ,6%. 1,,^ ( f.p'.e . 1 " . . ! i s annua l , o r o n c e per year .

' n- i I.''' y .>• i ''

n = 2 • 1 = 2 ; I, '.j!'!!'• • ' I <•/».'*•.' wn. - / < i

/ O C)w{n 5 I

22 7

/es tmen t is $22 727.12

20 000 = 2727 ,12

2727.12 o ; • = 0.136 356, .

20 000

Th -.lO of return o n the Bank A inves tmen t is 13.64¥o.

S - i r * R: T h e pr inc ipal is $20 000 .

luai in terest rate is 6 ,55%.

%i. . . ompound ing per iod is sem i -annua l , o r 2 t imes per year .

T h e te rm (in years ) is 2 .

n = 2 • 2 = 4

Ttie future value is unknown.

A = P(1 + if

A = 20 000(1 + 0 .0655)^

A = 22 7 5 1 , 5 4 0 . . . T h e future va lue of the i nves tmen t is $22 751 .54 .

22 751 .54 - 20 000 = 2751 .54

Rate of re turn ; = 0-137 577. . .

T h e rate of return on the Bank B inves tmen t is 13 .76%.

B a n k C : T h e pnneipa l is $20 000 .

T h e annua l in terest rate is 6 . 5 % .

T h e c o m p o u n d i n g per iod is quar ter ly , or 4 t imes per year .

T h e te rm (in yea rs ) is 2. n = 2 - 4 = 8


A = P(1 + if A = 20 000(1 + 0 .065) "

A = 22 752 .779 . . . T h e fu ture va lue of the inves tment is $22 752 .78 .

22 752 .78 - 20 000 = 2752 .78

R3,e of re turn: 0.137 639. .

T h e rate of return on the Bank C inves tmen t is 1 3 . 7 6 % .

T h e rates f r om grea tes t to least return on inves tment are

6 .5%. c o m p o u n d e d quar ter ly ( 13 .76%, Bank C) , 6 .55%.

c o m p o u n d e d semi -annua l l y ( 13 .75%, Bank B) , and

6 .6%. c o m p o u n d e d annua l l y ( 1 3 . 6 3 % , Bank A ) .

8. For $ 1 0 0 0 to g row v 3 n . 000 . it w o u l d doub le

four t imes .

a) X 4 = 48 ' 6

Us ing the rule of 72 . it wi l l take 4 8 yea rs for $ 1 0 0 0

to g r o w to $ 1 6 0 0 0 at an interest rate of 6 %

c o m p o u n d e d annua l l y .

b) I ? x 4 = 24 ' 12

Us ing the rule of 7 2 , it wi l l take 24 years for $ 1 0 0 0

to g r o w to $16 0 0 0 at an in terest rate of 1 2 %

c o m p o u n d e d annua l l y .

9. T h e in terest g r o w s by a bit m o r e t han $50 e a c h

year so I wi l l g u e s s that the pnneipa l w a s $800 .

Use th is va lue to de te rm ine the interest rate.

T h e pnne ipa l is $ 8 0 0 . The annual interest rate is unknown. T h e c o m p o u n d i n g per iod is annua l , or once per year .

T h e t e r m (in years ) is 3.

T h e fu tu re va lue $966 ,36 . I used the f inanc ia l app l i ca t ion on my ca lcu la tor ;

the annua l in terest rate is 6 .5%. Tes t t h e s e va lues to see if they p roduce the

cor rec t va lue of the i nves tmen t in year 2 .

T h e pnne ipa l is $800 . T h e annua l in terest rate is 6 .5%. T h e c o m p o u n d i n g per iod is annua l , or once per year .

T h e t e r m (in yea rs ) is 2.


I used the f inanc ia l app l ica t ion on my ca lcu la tor ;

the fu tu re va lue of the inves tment is $907 ,380 . .

If the pnne ipa l is $ 8 0 0 and the annua l in terest rate

is 6 . 5 % . the va lue of the i nves tmen t af ter two years

IS $ 9 0 7 . 2 8 , w h i c h is the va lue g iven in the tab le .

T h e in terest rate of 6 . 5 % and pr inc ipal of $800 are

correct .

10. F i r s t four y e a r s : T h e pnneipa l is $40 000 .


T h e c o m p o u n d i n g p e n o d is sem i -annua l , or twice per year .

T h e t e r m (in yea rs ) is 4 . n = 4 • 2 = 8

lt,o future value is unknown.

A - - . P I 1 + 0 " A ~ 40 000 (1 + 0 .048 ) "

A 4 0 3 5 7 . 0 3 2 . . .

T h e va lue of the i nves tmen t af ter four years is

$ 4 8 357 .03 L a s t two y e a r s : T h e pnneipa l is $48 357 .03 .

T h e annua l in terest rate is 6 % .

T h e e o m p o u n d i n g per iod is annua l , or once per year .

T h e te rm (in years ) is 2 ,

0 = 2 - 1 = 2 The future value is unknown.

A = P(1 + i f

A = 48 357 .032 . ..(1 + 0 .06) '

A = 54 3 3 3 . 9 6 2 . .

T h e tota l va lue of the i nves tmen t af ter six years is

$54 333 .96 ,

1-6 C h a p t e r 1: F i n a n c i a l M a t h e m a t i c s : Inves t ing Money

F i r s t f o y r y e a r s : T h e pr inc ipal , ]. i ...e. T h e annua l in terest rate is 9%.

T h e c o m p o u n d i n g per iod is semi-ânnual, o r 2 t imes per year

T h e t e r m (in years ) is 4 ,

0 = 4 - 2 = 8

The future value is unknown,

4 = P(1 + if

A = 1500(1 + 0.09)^

A = 2 1 3 3 , 1 5 0 . . .

T h e va lue of the inves tment af ter four years is $ 2 1 3 3 . 1 5 .

L a s t two y e a r s : T h e pr inc ipal is $2133 ,15 .

T h e annua l in terest rate is 1 1 % ,

T h e c o m p o u n d i n g per iod is month ly , or 12 t imes per year

T h e te rm (in yea rs ) is 2 .

,i o/ 2-1 The future value is unknown.

A = P{1 + if

A = 2133 ,15 (1 + OAlf*

/ I = 2 6 5 5 , 4 0 7 , . .

T h e tota l va lue of the inves tment af ter six years is $ 2 6 5 5 . 4 1 .

12 . a | e .g . . T h e h igher in terest rate is p a y m e n t in

e x c h a n g e for m o r e t ime be fore matur i ty .

b | i) 10 y e a r opt ion: T h e pnne ipa l is $5000 ,


T h e c o m p o u n d i n g per iod is annua l , or once per year .

T h e te rm (in years ) is 10,

0 = 1 0 - 1 = 10

The future value is unknown. 71 = P(1 + if

A = 5000 (1 + 0 .0325 ) ' °

A = 6 8 8 4 . 4 7 1 . . ,

T h e va lue of the inves tment a f ter ten years is $6884 .47 ,

F i v e y e a r t w i c e opt ion: T h e pr inc ipal is $ 5 0 0 0 .

T h e annua l in terest rate is 2 , 65%.



0 = 5 - 1 = 5


" - "'1 -r if

A 'f»00(1 + 0 . 0 2 6 5 ) ^

A ~ . ) t -98.555. . .

, . J lue of the inves tment a f ter f ive years is $5698 .56

R e i n v e s t e d : T h e pr inc ipal is $5698 .56 .

T h e annua l in terest rate is 2 . 6 5 % ,

T h e c o m p o u n d i n g per iod is annua l , or once per year

T h e te rm (in years ) is 5,

0 = 5 - 1 = 5

The future value is unknown. A - P(1 + if

A 5698 .56 (1 + 0 .0265)^

A - 6 4 9 4 . 7 0 6 , . ,

f h e va lue o f the inves tment af ter ten yea rs is $ 6 4 9 4 . 7 1 .

e .g. , Interest ra tes a re c o m p o u n d e d annua l ly , in terest

ra tes rema in the s a m e in 5 years , can re invest all

$ 5 6 9 8 . 5 6 in 5 yea rs .

I

i i | e .g . , T e n y e a r o p t i o n :

A d v a n t a g e _ _ ^ i s a d ¥ a n t a g e G IC interest rate is

secure if bank interest C a n n o t benef i t if bank

interest ra tes rise.

C a n n o t re invest the

m o n e y for ten years .

Don4 need to th ink

abou t inves tment for ten

years .

C a n n o t benef i t if bank

interest ra tes rise.

C a n n o t re invest the

m o n e y for ten years .

F i ve y e a r t w i c e o p t i o n :

A d v a t i t a g e D i s a d v a n t a g e • -OM h( nefit f r om h igher

terest ra tes

J invest ing.

Wi l l ea rn less interest if

bank in terest ra tes drop

af ter f ive years .

nvest money . In terest ra tes need to

rise over 3 . 2 5 % for total

i nves tmen t to ea rn

s a m e interest as ten

year op t ion .

eg. ,

f f 4 t n i l a r j D i f f e r e n t '~ \

Bofh inves tments pay ! 4 o m p o u n d inten-s?

If. terest as a percent ' •. . - 'estments a lso pay

the pnneipa l . j i ' sorest on prev ious

1 te res t ea rned . b i h inves tments can

h , ca lcu la ted us ing a |

i ^ imu la . 1

np io interest

es tmen ts a re eas ier

calculate b e c a u s e

ly have f ewe r

iables

Both inves tments

inc rease in va lue ovet

t ime.

' T j m p o u n d interest

es tmen ts inc rease in

va iue m o r e rapid ly than

s imp le interest

i nves tmen ts w i l h the

ne interest rate.

14 . a) T h e C S B P u d e e n buys in year 1 is inves ted

for 5 years . The C S B she buys in year 2 is

inves ted for 4 years , and so o n . T h e C S B she buys

in year 5 wil l be invested for 1 year .

De te rmine the yeady va lue of the f i ve-year C S B

then add the va lue r toqe ther

. Pr inc ipa l (J) ] \ ^ " "^^^0 ~ ^

fÂ^l^jA fâte pe rÂn j inm " " lJJ .02t l^ f

Penods per Year _ p

Va lue at E rid of Year _ [ ^ ~ ~

1 „ _^ J I y i i i f

„ J „ ^ 529 64 "

_ ^ ^ ^ ^ 545 I J ~ I ^ 561 03

0 ^ ^ 5 7 / 42 '

l o t n l ^ ? Z ^ Z - 8 i ^

T h e va lue of Pur ieen 's i nves tmen t a f ter f ive years is $2727 8 1 .


'><)()

2

2 / 2 / a i

5 9 4 2 4

f , l f 4 4

1441 41

4 4 7 9 4

hbi] H'y

4 H / 7 4^.

' " P i i n r . i p a l ( $ )

j | i4cror . t p f t A n n u m

I 14-ri(Kis |)f;r Y i ; a i

i V n l u e at t i i4 ..f Y e a r

1 ' 1 to ;>

r.

_ /

^ ~ 8 Z Z Z Z Z Z y

: ' 10

\ ' ' " k . r « !

; h . , v . i iut ; n-i irr . / f - . ' r .sf- i f a f tni t:;n y e a r ;

$5877 .96 .

I ' J ( - n v i n a n ; ».f of j «; . c - f.ui 4-'• i. >st 4f p: • <? (4

:,',< 4 . ivw i | . / 5 - . n t . . . \ i i I ' • 1 .' iti« ,<MV nt

• r n ; , r. 4 -/(-..iis ! f"- 4 i . fH; .i< i=c . . i , . , y.Mn> . . ^ u i ' 'f:

-ijfi. f.,j - 1- .', fifitif.if )!-•/»•!•./ '"AO 7 n n r ,

• c-;cin<<i. i r - i . ; •! K uf 4 i . - ! > - V C J I .Kjpussl . it ' '7

4 , . m n n , i ' i 4 4i^; d« t . ' rn l - 4 I ' H J i ' . O d

, i'.HH ip ii f 4 ; _

r c n » ! 4 s pof 7fM<

I V '5lu( . i l l m l <•> fe.Jf 4<ji

^ " 1} : tiC

L Z Z Z Z I ^ ^

i 4 , ^ 5 2 2 5-'

I r 4 ? f.4

T h e w of 4 nv"^- -n- f -oi tnt -nt a

$5168 .65 .

h . fa i Will-

i i '^pori t ".1

noi' Of-

4 on VIJ4V ni] i 4 2 2 4 2

^ 5 1 6 8 14»

H i s t o r y C o n n e c t i o n , p a g e 3 2

A. r . p . at the star t of t he 1950s , the interest rate w a s

2 5%. T h e interest rate i nc reased s low ly over the f irst

hal f of the d e c a d e a n d , by t h e end of the d e c a d e , it w a s

5%.

B. T h e best t ime to invest w o u l d have been at the end of

the 1950s , w h e n the in teres t rates w e r e at thei r h ighes t

for the d e c a d e .

A p p l y i n g P r o b l e m - S o l v i n g S t r a t e g i e s , p a g e 3 3

A I wil l start sav ing in 2 0 1 6 .

B. Resea rch resul ts

Sav ings accouru

GIC (1-year)

G I C ( S s y e a r l

C a n a d a Sav ings B o n d

, 1 bO%_

' 1 4 5 %

2 / 5 % _

0.65%

All t hese inves tmen ts c o m p o u n d dai ly .

C . I chose to invest my $ 5 0 0 0 in the 5-year G IC .

D Mv i n v r s t i n m i t m o l u r o d a l lo t 5 years : $ 5 7 2 5 . 9 6

Year

2 0 1 I

2 0 1 2

Ai I 1

4 0 1 5

2 0 I <.

S a v i n g s ( S )

5 0 0 0 0 0

148 '

5 2 8 0 6()

!)42f) BSf

5 5 / / 1 9

5 > 2 5 9 6

E . I ro l 'od ,i 1 M y i n v o s t i i i o n l ' s in terest rate

dfn n;o%f:d lo 1 / 5 ' 4 . .

F I i n v . v d f d III tne 5 yf.'or ' - . I ' . <.nce m o r e , s ince it

l i ,o . inn hifjlu.-i mien 'O f fnf(;

i i r ' n v f . . t f ' d m y ^.ovirvj ' - $4 /2- ' i 46 , and inves ted

$ 5 0 0 0 per yeat s ince my init .ai i nves tment for a

tota l of $30 725 .96 .

G . I r eached my goa l of 1 mi l l ion in 2128 , w h e n I

w o u l d be 139.

H. I no t iced tha t w h e n invest ing in a 5-year G I C , I

w o u l d not invest more m o n e y for ano ther 5 years .

W h e n I c o m p a r e d the resul ts of a 1-year G IC over

10 yea rs and a 5-year G IC over 10 years , I no t iced

that the 5-year G I C pe r fo rmed bet ter than the

1-year G IC on ly in the 10th year . There fo re , a

s t ra tegy that w o u l d resul t in the least age to reach

my goa l w o u l d have m e invest $5000 per year in a

1-year G IC for the first 5 - 9 yea rs to increase my

pr inc ipal as fas t as poss ib le . T h e n , I wou ld invest

in a ser ies of 5-year G I C s unti l I r eached my goa l ,

s ince the 5-year G I C y ie lds a h igher interest rate.

I. T h e o u t c o m e of the d ie roll a f fec ted my

inves tmen t m u c h more than the s t ra tegy I w a s

us ing , s ince my in terest rate w o u l d s o m e t i m e s d ip

be low 0, m e a n i n g my inves tmen t lost va lue .

J . S ince sav ings accoun ts , G I C s , and C a n a d a

Sav ings B o n d s d o not have negat ive interest ra tes,

it w o u l d m a k e sense not to let the rates go be low

ze ro . Moreover , the Bank of C a n a d a ad jus ts its

in terest rate based on in f la t ion, to keep inf lat ion

b e t w e e n 1 % and 2 % . D e p e n d i n g on the

inves tment , it w o u l d be reasonab le not to let ra tes

for the C a n a d a Sav ings B o n d go be low 0 .5% or

e x c e e d 5%. A n y d ie roll tha t w o u l d resul t in the

C S B rate go ing ou ts ide these l imits cou ld be

cons ide red as "no changeT

T h e s e mod i f i ca t ions cou ld m e a n that I cou ld reach

my inves tmen t goa l fas ter , s ince I wou ld never lose

m o n e y in any per iod . O n the o ther hand , it cou ld

a lso resul t in reach ing my inves tment goa l more

s lowly , s ince the interest rate on the C S B cou ld

never exceed 5%.

K. My mod i f ied ru les actua l ly dec reased the age at

w h i c h I r eached the goa l . Fo l lowing the inves tment

s t ra tegy of a 1-year G IC for the f irst 10 years , then

a 5-year G I C thereaf ter , I reached my goa l in 2 0 7 6 .

w h e n I w o u l d be 87 .

1-8 C h a p t e r 1 F i n a n c i a l M a t h e m a t i c s : Inves t ing Money

T o reach my goa l at a m o r e reasonab le age the ru les

cou ld be c h a n g e d to a l low a larger i nves tmen t each year

Or. the ru les cou ld be c h a n g e d to a l low an inves tment of

$ 5 0 0 0 in one 5-year GIC each year , ins tead of every 5 years .

L e s s o o i 4 • ^ ^ n p o u n c i I n t e r e s t : P r e s e n t ¥ a l y e p a g e 4 0

1 . Inves tment B wi l l requi re a g rea te r p resent va lue to be inves ted beeause the c o m p o u n d i n g f requency in less than for i nves tment A,

P = ^ ^ ^ ( T o / ) "

I n v e s t m e n t A : A = 10 000 , i = ^ , o = 120 12

10 000

1 + 0.05

12

P 6071 61

T h e present va lue of i nves tment A is $ 6 0 7 1 . 6 1 .

I n v e s t m e n t B: A = 10 000 , / = 0 .0125. n = 40

(1 + 0 . 0 1 2 5 ) *

P 6084.13

T h e present va lue of i nves tmen t B is $ 6 0 8 4 . 1 3

Inves tment B requ i res a h igher p resen t va lue .

S' i o v t - s f . j t e n t A : /-• -O ,1,'.'

P 6071.61 M ^ = 1647_, , / '

I n v e s t m e n t B :

A _ 10 000

P " 6084.13

643..

T h e future va lue to p resent va lue rat io for Inves tment A

IS 1.647. . . and for inves tment B is 1.643.. .

b ) T h e inves tmen t w i th annua l l y c o m p o u n d e d interest

w o u l d have a h igher rat io because the interest rate is

h igher a n d the pr inc ipa l is lower. Wi th a 6 % interest rate

c o m p o u n d e d annua l l y and a fu ture va lue of $10 000 the

p resen t va lue mus t be $5583 .95 . S ince the pr inc ipa l ' is

lower than both inves tment A and B, the rat io wil l be

higher.

3. R o w 1 : De te rm ine the p resen t va lue

P = ^

(1 + / ) "

A = 2 5 0 0 , / = 0 .078 , n = 8

T h e p resen t va lue is $1370 .85 .

7!'.r/ 2 . •. .e rmine the annua l in terest rate

• v a l u e is $ 2 0 0 0 .

•nterest rate is unknown.

' • • end ing p e n o d is sem i -annua l , or /ear.

0 f I. >..- (.., yea rs ) is 5

alue is $ 3 5 0 0 .

' ' m.; . ,4culator, the annua l in terest rate is 11 .5%. 11'.,%'} 3. I ) . i . j rmine the p resen t va lue .

^ = 0 . 0 0 6 . 0 = 4 8

va lue is $ 8 2 5 4 . 4 8 .

Ut.vj 4 I )• i--rmine the i nves tmen t t e r m ,

va lue is 609 .35 .

i t e res t rate is 13 .6%.

l d i n g per iod is a n n u a l , o r o n c e per

years) is unknown.

Iue is $100 000 .00 .

< 'rK, .;culator, the t e rm o f t h e i nves tmen t is

' ' 40 years .

f't'^-vi 5 o"- - om ine the annua l in terest rate

T h e p resen t va lue is $16 150.00.

The annual interest rate is unlinown.

T h e c o m p o u n d i n g per iod is month ly , or 12 t imes per

year .

T h e te rm (in years ) is 2.

T h e fu ture va lue is $23 500 .00 .

Us ing my calcu lator , the annua l in terest rate is 18 .9%.

4 . a) P

A = 260 000 , I = 0 .085. o = 20 p ^ _ 2 5 0 J ) 0 0 _

(1+ 0.085)"°

P 48 904.097. „

M a c shou ld invest $48 904 .10 n o w to have

$ 2 5 0 000 in 20 years .

b ) 2 5 0 000 ^ 4 8 904 .10 = 201 095 ,90

T h e inves tment wii l earn $201 095 .90 in in terest in 20 years

5. a) T h e present va lue is $ 9 0 0 0 .

The annual interest rate is unknown.

T h e c o m p o u n d i n g per iod is quar ter iy , or 4 t imes

per year.

T h e te rm (in years ) is 2 ,

T h e fu ture va lue is $17 000 ,

Josepp ie w o u l d need an annua l in terest rate of 3 3 . 1 % to mee t his goa l . Th is is not reasonab le . Cur ren t interest rates for sav ings accoun ts are 0 ,5% to 1.25%.

F o y n d a t i o n s o f M a t h e m a t i c s 12 S o l y t i o n s M a n u a l 1-9

b ) T h e p resen t va lue is $ 9 0 0 0 ,

T h e annua l in terest rate is 1 2 % .



T h e fu tu re va lue is $17 0 0 0 .

Us ing m y ca lcu la tor , it wi l l t a k e Joseppie 5.4 yea rs to have

$17 0 0 0 .

6. P A

( i Z T f

A = 17 50t : / o -.'28, o = 20

Cla i re has to invest $ 1 0 0 7 3 . 3 9 now t o have $17 500 in ten

yea rs .

T h e annua l inti • i l l I iMj,>'»

i n . :

0 = 6 - 1 = 6

A

>hf i>.ir:fi'i s/,m(f i . mknowr}.

. -,1 f.J,.- s 4 • ' }% |„>i i , 4 <% otot iK. once per year .

,11 - o >f> >.r

p =

(1 + fT

24 000

( l + 0 . 0 4 8 0 f

P 18 115.217. . ,

T h e p resen t va lue of op t ion A is $18 115,22 .

Interest e a r n e d : 24 000 18 115,22 - 5884 ,78

O p t i o n B : Tf ie present value is unknown.

T h e annua l in terest rate is 4 .75°4 .

T h e c o m p o u n d i n g per iod is sem i -annua l , or 2 t imes per year .

T h e t e r m (in yea rs ) is 6 y e a r s .

T h e fu tu re va lue is $24 000 ,

! i , r. M - i / o r

P_ p: 443 3 / 1 ,.

4 h o I o / . e r u v. i lue of opti<'i« % o 4 4 3 108.57.

I n i e i p s t f n m e d 24 0 0 0 ^ 18 103 3 / ^ 5 8 9 1 . 4 3

O p t i o n C : The present value is unknown.

T h e annua l in terest rate is 4 . 7 0 % ,

T h e c o m p o u n d i n g per iod is quar ter ty , or 4 t imes per year .

T h e t e r m (in yea rs ) is 6 y e a r s .

T h e fu ture va lue is $24 0 0 0 ,

24

A

^ (111) '

P 24 0 0 0 _

M i S ) 0 4 7 0 r

P 18 132,351. . ,

i f d e t e s i e c i m e d : 24 0 0 0 - i L35 = 5867 .65

O p t i o n

A

R a t e o f R e t u r n

3<384

4 3 1 13 22

3891 43

18^108 57

3 8 6 / , 6 3

18 132 35

(} .124 333

0 .',2^. ; r 7 )

f)..;2:!. (4)1

Opti.;r, B has IIlO y r f io tes i o 4 e of r rdon i at 32 3 3 ' 4

S a s h a shou ld c h o o s e op t ion B so tha t she ea rns

the mos t in terest on her i nves tment ,

b ) S a s h a w o u l d ea rn $ 5 8 9 1 . 4 3 on her i nves tmen t

by choos ing opt ion B.

O p t i o n A : e.g. . Inc rease the interest rate to fi% in par t h) and d e c r e a s e the interest rate to

8 T

1 n-y. ii

41 10 o<-<;

u '.7:H

; 35 one

o 070

<3 40!

4 0 1 * ' P r m o i p a l {%)

i n t e r e s t Ra te p p r

A i i m i m _ _ ^ _ ; _

P e r i o d s p e r ~feat^ I '

V a l y e at^EncJ o f Year

^ 1 4 101 C4> I • / 366 64 13 37o 4 /

^ ^ 17 443 2 ^ " 40 106 03_ _i 10 l / 2 ' » j i

~\'6'ik'1i'T 2 3 2 / 9 0 7 _ 1 0 i T T + \

20 214 «3< ' .-'fl 0^)1 90 • / 4 i l 52

41 780 i 3 ^ ' 2 i ;4 2 / ' 18 106.44

_6_

Ol. Mil

/ ' CO' 5

v. ri(.13

1 J'H !

ISOuC

1-CM.n

.(> SCO

i'OMiC

t r o O . r

Ye.its

( y e a r s !

0

^ 8

10

V a l y e o t i r i ¥ _ e s t m e n t i $ |

15 000 15 000

J6101:^»t )^ ! - '^Z i 0 4 ) M ^ V 4 T 1 2 8 • 30 100 68^ 1 8 761454 I " 2 ^ 2 79 0:3

20 2T4^83 , 2 6 OOJ .9<T 21 780 3 3 ^ 3 1 204.27

3=) „ T3JJ00

[ o "^fML. 10 172.90

16 793.31

1 / 4 ^ 7 . 5 2

18 106.44

1-10 C h a p t e r 1 : F i n a n c i a l M a t h e m a t i c s : I n v e s t i n g M o n e f

d ) T h e g r a p h s star t at the s a m e point . Inc reas ing the

in terest rate m a d e the g raph s teeper a n d it i nc reased

faster . Dec reas ing the in terest rate m a d e the g raph less

s teep and it i nc reased m o r e s lowly .

O p t i o n B : e .g . , Dec rease the pnnc ipa i to $20 0 0 0 in par t

b) a n d inc rease the pnnc ipa i to $30 000 in par t c) .

1 b ! a |

• i (...f l $ |

^ f i iS ' r i e< K o t o p.cr

' P e n . ••3-v p»'t Vr-,(t I

' yc ' i o . ; o l f u d Of Yr-or "

I 3 I 3 T 2 2 6 7 6 5

4 1 3 3 192.74

t

4^ 2 5 9 . 2 :

s* '.30/ / ,

"1 'j.-O 3f

'S 3 - 0 '

/ i 10 -0

' ; ; ."CO. Co

^o c .'. f •

o."

I / ': i / 0 , I ^

31 C

29 C

27 C

4? 25 C

J m 23 C >

GIC

21 C

19C

17C

15 Of

srest

Years

T i m e

(years)

Vai l T i m e

(years) pari

26 000

1 27 t. M'. ' to

2 29 3 / / 94

3 31 220 63

4 3 3 1 9 ' / -

3 35 23 ' . 03

• sm:O0!j4_,'

p.'-it ho

' / O OfH)

^ / 53 ' ?2

I 3 9 7 4 2

\}A 02U

2 ' 2 5 3 2 35_

^ / 4 W 43

30 ^)no

31 3,33 H

i 3T 4<.»6 ' 4 ,

j t i 030 4^,

38 23^9 28^

40 / 41 f,4

d ) e .g. . Chang ing the pr inc ipal d o e s not c h a n g e the s lope of

the g r a p h . Inc reas ing the pr inc ipal m o v e d the g raph up and

dec reas ing the pr inc ipal m o v e d the g raph d o w n .

O p t i o n C : e .g . . Dec rease the in terest rate to 3 % in part

b) and dec rease the interest rate to 2 % in part c ) .

3) b) ' c ) ' P r i n c i p a l ($) 8000 8000 8000

I n t e r e s t Ra te p e r

A n n u m

0.041 0T03 1 0 002

4 P e r i o d s p e r Y e a r 4 4

0 002

4

V a l u e a t E n d o f Y e a r

2

4

^ 6

" 8

^868(5

" 9 4 1 7 . 8 5

10 2 1 8 39

8492 / 9 8 3 2 5 66 2

4

^ 6

" 8

^868(5

" 9 4 1 7 . 8 5

10 2 1 8 39

90 15 94 8664 57

2

4

^ 6

" 8

^868(5

" 9 4 1 7 . 8 5

10 2 1 8 39 9571 41 9017 28

2

4

^ 6

" 8 1 1 086 99 10 160 .89 \ 9384

GIC Investment Value per Year

terest

terest

terest

OOi.iiS I i j .

;i5-4-o ny

\:IOOm C;0

p. i r f o r • :->Ol>0 00

lart c)

1000.00

3325 .66

1664,57

9 0 1 7 . 2 8

1384.34

d ) T h e g raphs star t at the s a m e point. Dec reas ing the

in terest rate m a d e the g raphs less s teep and they

inc reased more s lowly . T h e d is tance be tween points in

the s a m e year b e o a m e larger as t ime i nc reased .

9. Op t ion C wi l l a l low Blake to invest the least a n d

still m e e t his goa l . It had the h ighest annua l

in terest rate and the second mos t f reguen t

c o m p o u n d i n g per iod .

O p t i o n A : The present value is unknown.


T h e c o m p o u n d i n g per iod is a n n u a l , or once per

year .

T h e te rm (in years ) is 40 years .

T h e future va lue is 1 000 0 0 0 ,

n = 4 0 . 1 = 4 0

( 1 + 0 "

I non fj i jO

' . 1 0 l y o )

r 0 6 / H 3 9 3 . .

1 hc p i esen t va lue of opt ion A is $8678 .89 .

O p t i o n B: The present value is unknown.


T h e c o m p o u n d i n g penod is sem i -annua l , or

2 t imes per year .

T h e te rm (in years ) is 4 0 yea rs .

T h e fu ture va lue is 1 000 000 .

o = 40 2 = 80

F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l 1 1 1

I

A ^

1 ono 000

n ! 0 ! I O I

r OHI:',

I I H ; pt<-:.fjil v a l u t ; o l op t ion B IS $9815 ,74 ,

O p t i o o C : I In - pii-r:{int value is unknown.

111.. on i i i i , i l i i i lon ;,l ta te is 1 3 . 2 % .

1 h r <,()nipf)un4inq p j j r iod is quar ter ly , or 4 t imes per year .

! Ill - if-nt! (iii y ! - .n- , j is 4 0 years .

Int.- l u l l . ! / ; v ; i !os; I , ! 0 0 0 0 0 0 ,

n = 4 0 - 4 = 160

( 1 + i T

I OOP 000

• M- 1 3 2 f °

P = 5545.600. . ,

T h e p resen t va lue of op t ion C is $5545 .60 .

O p t i o n D: The present value is unknown.


T h e c o m p o u n d i n g per iod is week ly , or 52 t imes per year .

The r-r, Un yea rs ) is 4 0 years .

T h e t o t u r e > a lue is 1 0 0 0 0 0 0 .

n = 4o -- 2080

3 000

M i l l 1153)"

P = 9982.772, , ,

T h e p resen t va lue of op t ion D is $9982 .77 .

Op t ion C has the lowest p resen t va lue, so it is the best

op t ion for B lake .

10 . F ranco m a d e the g r e a t e r original i nves tment

because inves tmen ts w i th a n n u a l c o m p o u n d interest

earn less than inves tmen ts with month ly c o m p o u n d e d

interest (and the s a m e a n n u a l interest rate) .

Dav id

Future Va lue (S;

Interest Rah oer

A n n u m

Penods per Year

N u m b e r of Yea rs

Presen t Va lue ($)

r j r i j H yy

2 5 oo r r

0 04'<

.40

i T T ' ~ 7 6 0

2 0 4 2 f l

_ 25 000

i 0 06O

I 7 0 1 1

1^5 47 'MO

3 3 7 7 . 6 0 - 3 1 / 4 ] 4 0

Franco inves ted $ 2 0 4 . 2 0 more t h a n Dav id .

1 1 . a) T h e p resen t va lue is $3000 .




T h e fu ture va lue is $ 7 0 0 0 .

I used the f inanc ia l app l i ca t ion o n my calcu lator : Lucy

needs an annua l in terest ra te of 8 .56% to mee t her goa l .

I

OHIO

UH H)

.t'iO

C O , lh«> i.i lK. -Aouid d e c r e a s e if the interest we re

comp(« ;nd . -d . ini ia<4ly, A tower e o m p o u n d i n g

fre q u o i n , y -Aoold . e d u c e the fu tu re va lue but not

c h a n g e She pn-r .cm va lue , mak ing the rat io smal ler .

Th t ; pio-scnl va lu t ; is $ 3 0 0 0 .

The* onnu. i l >Mterf.si rate is 8 . 56%.

T h e f-.dmpfJoodiiK) oer iod is a n n u a l , or o n c e per year .

T h e f e : i n («n y e . H . o is 10 yea rs .

n = 10 - 1 = 10

F4f," thfiift J iKie is unknown

A ' ' ( I t

A >oo(4 I ^ ' ) .0856)^°

'» - f.32(S '•-'> .

lh' f i j k ' i e v . 4 , e of the i nves tmen t w i th in terest

eoi:,f.,,.u :4f o .mnua l l y is $ 6 8 2 0 55.

", O.'O-'I'OS

I' 3000

273. .

It.' IvK. dec ima l p laces , the rat io w o u l d d e c r e a s e to

12 . The present value Is unknown.


The c o m p o u n d i n g per iod is month ly , or 12 t imes

per year .

The t e r m (in yea rs ) is 0 75 years .

T h e fu tu re va lue is $ 4 7 6 5 . 3 0 .

0 = 0 . 7 5 - 12 = 9

A

(Uif

.30

• 1 + 0 053 )

r 4 3 / 9 995, , ,

T h e prf;<^eiit va lue of Dan ie l ' s i nves tmen t is

$4579 .995 . .. o r $ 4 5 8 0 .

4765 .30 - 4 5 7 9 . 9 9 5 . . . = 185 ,304 . . .

T h e accoun t has e a r n e d $185 .30 in interest .

13 . The present value is unknown.


The c o m p o u n d i n g per iod is sem i -annua l , or

2 t imes per year .

T h e te rm (in yea rs ) is 10 years .

T h e future va lue is $15 000 ,

n - 10 2 ^ 20

A

i l j f

15 000 P

{1 I 0 0 5 5 ]

8 / 1 8 76,. ,

1-12 C h a p t e r 1 : F i n a n c i a l M a t h e m a t i c s : I n v e s t i n g M o n e y

• >'• h - . i f j ; ! . . , ,

" T . - . l i . Uf,- ^ l > . - . H , . . . , : l , . i , , , . , . , , . . , ; . , , , j

.•:-,<,I.!.i i: i l,,..

r-< . { I ^ i r j , - : - ' : . » , ! { „ „ , , . ,

• ' ^ " • ' " ' • l ' ^ - . ' y ' ' ; ' , . f l , . ; M . , . f t i - ^ . e- f -Mf . •

$ 1 0 0 SO m y fu ture va lue ' V I -/'III

T h e p resen t va lue is $100 .

' ' " - O ' " - ' Imo pc o - . ' , c,-,- r ter iy, or 4 t imes per year

T h e fu ture va lue is $ 3 0 0 .

- I ,n m y calcu la tor ; A n ' m - u , - . . r - i . ' • „ 0 y o . ,v..-i -,:f<„v the investment to tr iple n-'Oiy 1 ' y.-j,-.,

•^ i a j : h ) p o " 1,1-; j.ilm .< -nl i .pO. f h o .mr ioo l mh r-'-sf lo fe r.

Ihv c o o i p f o o O i o o p . T M O , oo t ioa l , o r once per year T h e Lone ur. 4 i

r i i e *i|f i,|r. vo luo c4 If..-; ... . • i -4 iOfnt is $ 1 0 5 0 .

b | i | t h f p o - . o m v i ' . K . r , .31404

h'u: n.'.ntiaf I'liLic J r.jlv >. niikn^wn.

Tiif- t o n : p o u n U i n y p^ouci lo se iu i -annua l . o r 2 times per year .

T h e te rm ( in yea rs ) is 1 year .

T h e fu tu re va lue is $ 1 0 5 0 ,

T h e annua l interest rate is 4 . 9 4 % .

i i | T h e present va lue is $ 1 0 0 0 .


T h e compounding period is quar ter iy . or 4 t imes per year T h e te rm (in years ) is 1 year, ^ ^

T h e fu ture va lue is $ 1 0 5 0 . T h e annua l interest rate is 4 ,91 % i i i ) T h e present va lue is $ 1 0 0 0 .


T h e compounding per iod is monthly, o r 12 times per year

T h e te rm (in yea rs ) is 1 year, ^


T h e annua l interest rate is 4 . 8 9 % .

' f - 'I 0 . |r„v.-: .n l . -K- .M,J le V./.I4 „ . , . „ j ; " 4 " ' <" .Hj , r , „ . ,d i , , . , - / o i . c . n . n r .

'•' f •• " * • •• fop'Hind ;o' -,...,{ , . . „ j . . , , „ fh,

' ' • • / • - • " 'In a! .1 3. ,hi I ii;|..N •.» i , ip . wi!r. ' •' ' Ol" -U' ' ,.; p...l,,0,r,.j I j , . , . , , , „ ^ , ,, j ^,1^, • m,. : .• ,t , . . , . 1

M i c l - t 3 l i o p t e « fipvhim. p a c j e 4 5 '. A / /

' ' $ ' / I . 31 .n , 0 , t i ,) ' ' ' • " 30 t ..r><4/|} oo(».|-;,/, ..-O Oil • : U Hi!

lO.O'

' '• 3 (M.s.tif 1 V- ir '

' ' " . T ' ' ! ; ' o - 3of :4- j , r o f / 0- - i .H

' ' ' f • " • • 'T ' *:..• I'llf O' 4 .viii bl.' ,,.-i,4 oo< <i4

' 'O o ,if,.p

< Of KorOfr^ifsr /» j , 4S..4: , . , : y i j , / , c--, ,

•= * '33 5 " 3 r 5 '-o !.;•.-,,,.•

T ^ » 5 iO 3 3't • 4 ) ( 1 ; ,

• • '•• 0:o , 'c., i , i . , „ „ ^ 4 i . , V.400 01 A at, the no./. v,4ue -4 f 4 K r h n<H/v yea , Use a l a b h ; •© ' - m o o , . - 4.',- , io- .v. . . r . CAmx: va lue- , have been ') f !c!S'4 t

! ^ ' n r . c i p a l ($)^ | Y e a r ^ e n a Valwe j f • i ^ 5 0 9 0 00 T " ^ ^ - :

J /6Ci9. i r .

^T' _ _ . J ? 335 79

K.4hoi.r!e'<-.,«.(oor-r mil f,e m'rj.ff, $ j 1 gj j .^ a f ter 20 yea i s .

B r a d P r. I h o o o , / is ,^ ,3% or 0.055; / is 1 ^ 10 13, 411 - - .

4 ^ p( I r ,|)

Y e a r " rP r i r i c i j , a l i $V

5 0 0 0

z z z m i o

5 0 0 0 _^ _

Brad 's account wil l he wor th $10 500 aHer 20 years .

5243 .39

0341 32

8 0 4 2 47^

10199 98

12 936 27"

5

15~

2 0 "

.5275

6 3 7 5

_ ^ 7750

9125

1 5 5 0 0 ^

1-13

1)1

f ,itl-. IH'. i;v'.-.iiii- r;l

I J__L_|.-l~|——i_i_4—4—4--|

: . . I . . ; - \ ^ |. ,th.'>i,ie's

-UKHi

: c-iin

' . nil'I

;.;)<•<) *

; -«;.';

•, • sf .

s 000 4

^ , n O - " " ' '/.ih>i: «.t |!iV0'-4lJ.p-!l { 4 ]

{./...lO-i ! r .o ' j . - 'ooe 1 j i i a c

, ' 0 )041 4,4

'; ^ " 804 4 r '

! ' ' 14"44I3 47

c ) T h e in tersect ion point on tne g rap i i n-Oi^ see.- , ti

po in t at w h i c h bo th i nves tmen ts ea rn tt.- ^^n'v.. -m-

of interest.

44

1!i

-4»

5 2 7 5 J

4- >!:•• '

<M4.n j

1040'.! I

4 . a) T h e pnnc ipa i is $ 3 0 0 0 .

T h e annua l in terest rate is 5,6¥o. T h e c o m p o u n d i n g per iod is annua l , or once per year .



T h e fu ture va lue o f t h e G I C is $ 5 1 7 3 . 2 1 .

b) $3000 wi l l doub le tw ice to b e c o m »0.

1 ^ x 2 = 25.714. . . 5 6 It wil l take abou t 25.7 yea rs for the i nves tmen t to be

wor th at least $12 000 .

c ) i) e g . , If the c o m p o u n d i n g f r eguency inc reases to

month ly , the fu ture va lue of the i nves tmen t wi l l inc rease.

M o r e f reguen t c o m p o u n d i n g resul ts in more interest

be ing e a r n e d . T h e pnnc ipa i is $3000 ,

T h e annua l in terest rate is 5 .6%,

T h e c o m p o u n d i n g p e n o d is month ly or 12 t imes per year .


The future value is unknown. T h e future va lue of the G I C is $ 5 2 4 5 . 1 8 . Th is is more

than the ong ina l fu ture va lue of $ $ 5 1 7 3 . 2 1 .

ii) e g . . If the interest rate c h a n g e d to 2 . 8 % c o m p o u n d e d

semi annual ly , the fu tu re va lue of the i nves tmen t w o u l d

dec rease . A lower in terest rate m e a n s less interest wi l l

be ea rned on the inves tment . T h e c h a n g e f r o m annua l to

semi -annua l e o m p o u n d i n g wi l l not af fect the fu ture va lue

as m u c h as the interest rate be ing reduced by half.



! i „ > , o i H p . n i u u l o o o« ' " " J 1 . • <-m: 'Hnual . or 2

S ine - P'-r y<-,)i : t , f U i U i i in \-'•<»'•.) ' n

llu'lutulf i o / i / . I - . .inknimif

i l i , , h . h i i . - v o l o . <,l Ih i - t , . iO 1- > . 0 6 1 , 6 9 , Th is is

I. ..,', t h .m the noo - n . i i Intn. ' . ' v,,lo;- )f $5173 .21

d ) lh ( oo iu ip.)l I . S ioOO II. ,-.iiutu.il inti't'-'st i-th'v uiiiuMivjn.

l l i e . o , u o < , u n d m o p. r i c d • . 4 ,.lv. or 365 t imes per year.

1 h e ! o i n i (ill y e . i O . )

I I H l o t o i e -o i loe IO $ ' . , ' / • • '

An loO-ie: t f ; i le ef S 04 'S t.-'-e<led tO have 3

i . l tu ie ./.jlO.- •-: 1,1'.'/ '> 31

5 I h e pue,, ip.i l :s 3 ' . ! ' OOO

Puo . lu in ia l mt. 'H '.t n i t e r, / /-. '.s < Ur. , ,o ioo<.nn4 !n ( j p. n "4 - , i;- . . , idorly, or 4 t imes per year .

I 4 o l e r m n a -i-v.wA '',

Ihe tuiuiti vdluv IS uiiktiuhMi T h e fu tu re va lue of the i nves tmen t is $62 947 .39

62 9 4 7 . 3 9 - 50 000 = 12 947 39 The re wi l l be $12 947 .39 ava i lab le for spor ts

e g u i p m e n t at the end of 3 years .

S. I n i t i a l I n v e s t m e n t : T h e pnnc ipa i is $ 1 0 0 0 .

T h e annua l in terest rate is 5%.



The future value is unknown. C . O T ^ ^ O R

T h e fu tu re va lue of the init ial i nves tment is $ 1 2 7 6 . 2 8 .

Opt ion A : T h e pnne ipa l is $ 1 0 5 0 .

T h e annua l in terest rate is 5%. T h e c o m p o u n d i n g per iod is annua l , or o n c e per year .



T h e fu tu re va lue of op t ion A is $ 1 3 4 0 . 1 0 .

Opt ion B : T h e pnnc ipa i is $ 1 0 0 0 .

T h e annua l in terest rate is 6 % . T h e c o m p o u n d i n g p e n o d is annua l , or o n c e per year .



T h e future va lue of op t ion B is $ 1 3 3 8 . 2 3 .

Opt ion C : T h e pnnc ipa i is $ 1 0 0 0 .

T h e annua l in terest rate is 5%. T h e c o m p o u n d i n g p e n o d is month ly , or 12 t imes per

year. T h e t e r m (in yea rs ) is 5.


T h e fu tu re va lue of the op t ion C i s $ 1 0 3 , 4 3 6 .

Opt ion D: T h e pnnc ipa i is $100

T h e annua l in terest rate is 5%. T h e c o m p o u n d i n g per iod is annua l , or once per year .



1-14 C h a p t e r 1 : F i n a n c i a l M a t h e m a t i c s : Inves t ing Money

•' • , . ;! ,t . •: I II • ,"l , 1 . J! 1, , . ,1, T h e n e w inves tment has a h igher rat io than the ong ina l inves tment .

I = '-'l'-':; . , - ; . „ .j . . i O^ I . - .0) ; T

I ' T ' l i ' " . M _ . r (• h , . i , - ' . , lo -0 "

•H'-tJ'- /• i . . 1 . . l . O . • . I ,,r. 4, ' i ,r-| I ,

:••"'"'-< • >'''• ,(• . .' , !;,.- S - p^,,- i,

impact ,

7. a | The present value is unknown.

The annua l in terest rate is 6%,

T h e compoonc i ing per iod is month ly , or 12 t imes per year t e rm (in yea rs ) is 3 years .

T h e fu ture va lue is $10 000 ,

Des i ree shou ld invest $ 8 3 5 6 . 4 5 to have $10 000 in th ree years ,

b} The present value is unknown.

The annua l in terest rate is 6 % .

c o m p o u n d i n g per iod is semi^-annyal, or 2 t imes per year term (in yea rs ) is 3 years .

T h e fu ture va lue is $10 000 .

Des i ree shou ld invest $ 8 3 7 4 . 8 4 to have $10 000 in th ree years .

8. a) 1) The present value is unknown. T h e annua l in terest rate is 7 .2%,

T h e c o m p o o n d i n g per iod is annua l , or once per year T h e te rm (in yea rs ) is 22 years .


T h e ongma l i nves tment w a s $2382 9 1 .

i i ) The present value is unknown


T h e c o m p o u n d i n g p e n o d is sem i -annua l , or 2 t imes per year T h e te rm (in years ) is 22 years .

T h e fu ture va lue is 3 i i K, i.

T h e ongma l i nves tment w a s $2320 .40 .

b ) T h e rat io w o u l d be h igher because the c o m p o u n d i n g is

more f requent .

T h e pnnc ipa i is $11 000 .


T h e c o m p o u n d i n g p e n o d is month ly , or 12 t imes per year



T h e fu ture va lue of the inves tment is $53 365 .38

Orig ina l i n v e s t m e n t :

j . A ^ 11 000 .00 ^ ^ 1 1 000.00

P 2382 .91 ' P 2 3 2 a 4 0 "

f = 4,616. . . 1 = 4.740. , ,

New i n v e s t m e n t :

A ^ 53 365 .38

P 11 000 .00

^ = 4 . 8 5 1 . . .

9. T h e pr inc ipal is $400


T h e c o m p o u n d i n g per iod is month ly , or 12 t imes per

year .


T h e fu ture va lue is $625 .

T h e annua l in terest rate is 4 . 4 7 % .

10 . $250 wi l l doub le tw ice to b e c o m e $ 1 0 0 0 .

It wi l l take abou t 24 years for the $ 2 5 0 inves tmen t -ow to $ 1 0 0 0 .

pr inc ipal is $ 2 5 0 .

annua l in terest rate is 6%.

c o m p o u n d i n g per iod is sem i -annua l , o r ••oes per year.

term (in years) is unknown.

fu ture va lue is $ 1 0 0 0 .

It wi l l take 23 .45 years , or 23 .5 yea rs for the $250

inves tment to g row to $ 1 0 0 0 .

L e s s o n 1 .5 : I n v e s t m e n t s I n v o l v i n g R e g u l a r

P a y m e n t s , p a g e 5 5

1 . a) T h e regu lar p a y m e n t a m o u n t is $ 2 0 0 .

T h e p a y m e n t f r eguency is month ly , or 12 t imes per year T h e n u m b e r of paymen ts is 600 .

T h e paymen ts are m a d e at the end of each

p a y m e n t p e n o d .

T h e annua l in terest rate is 4 . 8 % ,

T h e c o m p o u n d i n g f reguency is month ly , or

12 t imes per year.


T h e fu ture va lue of the inves tment is $ 4 9 8 526 .60 . b | T h e regular p a y m e n t a m o u n t is $ 1 7 5 0 . T h e paymen t f reguency is sem i -annua l , o r 2 t imes per year .

T h e n u m b e r of paymen ts is 40 ,

T h e paymen ts are m a d e at the end of e a c h



T h e c o m p o u n d i n g f reguency is sem i -annua l , o r

2 t imes per year.


T h e fu ture va lue of the inves tment is $126 127 32

c) T h e regular paymen t a m o u n t is $50 . T h e p a y m e n t f r eguency is quar ter iy or 4 t imes per year T h e n u m b e r of paymen ts is 160. T h e paymen ts are m a d e at the end of each p a y m e n t per iod T h e annua l interest rate is 8 .4%, T h e c o m p o u n d i n g f reguency is gua r tedy or 4 t imes

per year.


The fu ture va lue o f t h e inves tment is $ 6 3 820 ,79 , d ) The regular paymen t a m o u n t is $ 5 5 0 0 ,

T h e p a y m e n t f r equency is sem i -annua l , or 2 t imes per year .

F o u n d a t i o n s of Ma themat ics 12 S o l u t i o n s Manual 1-13

T h e n u m b e r of p a y m e n t s is 24 , T h e p a y m e n t s are m a d e at the end of e a c h p a y m e n t

pe r iod . T h e annua l in terest rate is 6 .5%, T h e c o m p o u n d i n g f requency is sem i -annua l , o r 2 t imes

per year . Tf ie future va lue is ur^known. T h e fu ture va lue of the i nves tmen t is $ 1 9 5 389 .47 ,

2. a) T h e regu lar p a y m e n t a m o u n t is $ 1 0 0 . T h e p a y m e n t f r equency is month ly , or 12 t imes per year .

T h e n u m b e r of p a y m e n t s is 72 T h e p a y m e n t s a re m a d e at the end of e a c h p a y m e n t

per iod . The annual interest rate is unknown. I used the f inanc ia l app l ica t ion on my ca lcu la tor : T h e

c o m p o u n d i n g f r equency is month ly , or 12 t imes per year .

T h e fu tu re va lue is $ 7 8 0 0 . 6 1 .

T h e in terest rate is 2.683o. b) The regular payment amount is unknown.

T h e p a y m e n t t r equency is sem i -annua l , or 2 t imes per

year . T h e n u m b e r of p a y m e n t s is 14. T h e p a y m e n t s are m a d e at the end of e a c h p a y m e n t

p e n o d . T h e annua l in terest rate is 3 .5%,

T h e c o m p o u n d i n g f r equency is sem i -annua l , o r 2 t imes

T h e fu ture va lue is $3927 ,38 ,

I used the f inanc ia l app l ica t ion on my ca lcu la tor . T h e

p a y m e n t a m o u n t is $250 . c ) T h e regu lar p a y m e n t a m o u n t is $20 000 . T h e p a y m e n t f r eguency is quar ter iy or 4 t imes per year .

The number of payments is unknown.

T h e p a y m e n t s a re m a d e at the end of each p a y m e n t per iod . T h e annua l in terest rate is 4 , 7 5 % . T h e c o m p o u n d i n g f reguency is quar ter ty or 4 t imes per

The ' f u tu re va lue is $1 0 5 4 9 7 0 . 0 1 . I used the f inanc ia l app l ica t ion on my ca lcu la tor : T h e n u m b e r of p a y m e n t s is 41 .199 . .. so the te rm is 10.3

yea rs .

3. T h e regu lar p a y m e n t a m o u n t is $ 3 5 0 . T h e p a y m e n t f r equency is month ly , or 12 t imes per year .

T h e n u m b e r of p a y m e n t s is 216 . T h e p a y m e n t s a re m a d e at the end of each p a y m e n t

per iod . T h e annua l in terest rate is 7 .2%. T h e c o m p o u n d i n g f requency is month ly , or 12 t imes per

year . The future value is unknown. T h e fu ture va lue of the inves tment is $ 1 5 4 030 .54 , Interest : 154 030 .54 - (216) (350) = 78 430 .54 Dar iene e a r n e d $78 430 .54 in interest .

4. I nves tmen t A wi l l ea rn m o r e in terest t han

inves tmen t B b e c a u s e the $ 5 0 0 0 ea rns interest for

the ful l f ive yea rs wh i le four $ 1 0 0 0 p a y m e n t s ea rn

in terest for less than f ive years . I n v e s t m e n t A : T h e pnnc ipa i is $ 5 0 0 0 .

T h e annua l in terest rate is 6 % . T h e c o m p o u n d i n g p e n o d is annua l , or once per

year . T h e te rm (in years ) is 5 The future value is unknown. T h e fu ture va lue of i nves tmen t A is $6691 13.

Interest : 6691 .13 5000 = 1691.13 Inves tmen t A e a r n e d $1691 13 in interest .

I n v e s t m e n t B: T h e regu lar p a y m e n t a m o u n t is

$1000 T h e p a y m e n t f r eguency is annua l , or once per

year . T h e n u m b e r of p a y m e n t s is 5. T h e p a y m e n t s a re m a d e at the end of each

p a y m e n t p e n o d . T h e annua l in terest rate is 6 % . T h e c o m p o u n d i n g f r equency is annua l , or once per

year . The future value is unknown.

T h e fu tu re va iue of t he i nves tmen t is $5637 .09 .

Interest : 5637 .09 - (1000) (5 ) = 637 .09

Inves tment B ea rned $637 .09 in interest .

Inves tment A earns m o r e in terest than

inves tment B.

5. T h e regular p a y m e n t a m o u n t is $600 , T h e p a y m e n t f r equency is quar ter ly or 4 t imes per

year . T h e n u m b e r of p a y m e n t s is 20 . T h e p a y m e n t s are m a d e at the end of each

p a y m e n t per iod . T h e annua l in terest rate is 8 % . T h e c o m p o u n d i n g f requency is qua r tedy or 4 t imes

per year . The future value is unknown. Fraser wil l have $14 150.77 w h e n he is 2 1 . Interest : 14 150.77 - (600) (20 ) = 2150 .77 Fraser ea rned $2150 .77 in interest .

6. The regular payment amount is unknown. T h e p a y m e n t f requency is month ly , or 12 t imes per

year . T h e n u m b e r of p a y m e n t s is 24 , T h e p a y m e n t s are m a d e at the end of each

p a y m e n t pe r iod . T h e annua l in terest rate is 6 % . T h e c o m p o u n d i n g f r equency is month ly , or 12

t imes per year . T h e fu ture va lue ts $ 5 0 0 0 . I used the f inancia l app l ica t ion on my calcu lator : Z o e y m a d e regular depos i t s of $196 .60 .

1-16 C h a p t e r 1: F i n a n c i a l M a t h e m a t i c s . Inves t ing Money

Rate of return =

7. a) i | The regular payment amount is unknown.

The p a y m e n t f r equency is month ly , or 12 t imes per year .

T h e n u m b e r of paymen ts is 4 2 0 .

T h e p a y m e n t s are m a d e at the end of e a c h p a y m e n t

p e n o d .


T h e c o m p o u n d i n g f requency is month ly , or 12 t imes per

year .

T h e fu ture va lue is $1 000 000 .

J a y n e needs to invest $76 22 at the end of each m o n t h .

ii) The regular payment amount is unknown.

T h e p a y m e n t f r equency is month ly , or 12 t imes per year . T h e n u m b e r of paymen ts is 4 2 0 .

T h e p a y m e n t s a re m a d e at the e n d of e a c h paymen t per iod .

I ho- annua l in terest rate is 6 .9%,

T h e c o m p o u n d i n g f requency is month ly , c • hmes per year .

T h e fu tu re va lue is $1 0 0 0 000 .

J a y n e needs to invest $568 .60 at the end of each m o n t h , b) Opt ion i):

Interest ; 1 000 0 8 8 . 0 5 (76 .22) (420) = 968 075 .65

9 6 8 0 7 5 6 5

32012 "40

Rate o f return = 30 .240 6 4 5 , , .

Op t ion i) rate of return is 3 0 2 4 . 0 6 % .

Opt ion ii):

Interest : 1 000 008 .39 - (568 .60) (420) = 761 196.39

761196.39

'23"8812

Rate of return = 3.187 4 2 9 . , .

Op t i on ii) rate of return is 3 1 8 . 7 4 % ,

J a y n e shou ld c h o o s e opt ion i) s ince the rate of return is

a lmos t ten t imes greater than the rate of return for op t ion

ii).

8. a) T h e regu lar paymen t a m o u n t is $25

T h e p a y m e n t f r equency is month ly , or 12 t imes per year . T h e n u m b e r of paymen ts is 60 .

T h e p a y m e n t s a re m a d e at the end of e a c h paymen t per iod .


T h e c o m p o u n d i n g f reguency is month ly , or 12 t imes per

year .


At the end of f ive years , the fu ture va lue of Aa ron s

a c c o u n t is $1665 .90 .

b) The present value is unknown.




T h e fu ture va lue is $1665 .90 .

T h e p resen t va lue is $1348 .02 .

C a s e y inves ted $1356 .16 .

c ) A a r o n ' s i nves tmen t wil l be wor th m o r e at the end of

10 yea rs b e c a u s e he is mak ing more f reguen t depos i t s

a n d the interest is c o m p o u n d e d more o f ten .

Ra te of return =

A a r o n : T h e regu la r p a y m e n t a m o u n t is $25

T h e p a y m e n t f r e q u e n c y is month ly , or 12 t imes per year .

T h e n u m b e r of p a y m e n t s is 120.

T h e p a y m e n t s a re m a d e at the end of each



T h e c o m p o u n d i n g f r equency is month ly , or 12

t imes per year .


At the end of f ive yea rs , the fu ture va lue of Aa ron ' s

accoun t is $ 3 7 2 0 . 3 3 .

C a s e y : T h e p resen t va lue is $ 1 3 5 6 . 1 6 .


The c o m p o u n d i n g per iod is annua l , or once per

year .



At the end of f ive yea rs , the future va lue of Casey ' s

accoun t is $ 2 0 4 6 . 3 9 .

Aa ron ' s i nves tmen t is wo r th more t han C a s e y ' s

inves tment .

9. T h e regu lar p a y m e n t a m o u n t is $ 5 0 0 .

The p a y m e n t f r e q u e n c y is month ly , or 12 t imes per year.

T h e n u m b e r of p a y m e n t s is 60 ,





t imes per year .

T h e fu ture va lue is $ 3 5 000 ,

I used the f inanc ia l app l ica t ion on my ca lcu la tor :


10. T h e regu lar p a y m e n t a m o u n t is $ 1 0 0 0 .

T h e p a y m e n t f r eguency is sem i -annua l , o r 2 t imes per year .

The number of payments is unknown.


paymen t p e n o d .

The annua l in terest rate is 7 .5%.

T h e c o m p o u n d i n g f reguency is sem i -annua l , or

tw ice per year .

The future va lue is $10 000 .

I used the f inanc ia l app l ica t ion on my ca lcu la tor : It

wil l take 8.65 p a y m e n t s or 4 .33 yea rs for the inves tment to be wo r th at least $10 000 .

11. Dee : T h e regu lar p a y m e n t a m o u n t is $1000 .

T h e p a y m e n t f r eguency is month ly , or 12 t imes per year . T h e n u m b e r of p a y m e n t s is 60 .

T h e p a y m e n t s are m a d e at the end o f e a c h p a y m e n t

per iod.

The annua l in terest rate is 4 % .

T h e c o m p o u n d i n g f r eguency is month ly , or 12 t imes per

year.


At the end of f ive years , the fu ture va lue of Dee 's accoun t is $66 298 .98 .


P e t e : H»e l i - . j t i i . i ! (s . ivH'et i l n i n i . i i n ! i . e

I h i - p . i v i n e n i t r f i | U f i i e v KH' i i ihSv er 1 ti>fn,-, per year ,

i lit- .niMiher of [ . . ivmenl- . r. h-'fi

J h.- pay ine i i ! - , a te f i ieh. - a l l l ie .-nh el i-a» |. p, ryment

Oen-.xl I ti< . i i i i i ea l int«,'ie-.l i a l e r. 1' '.. I he e . n i i p e u f i l i n q !i»;(]uent y i'- r:>i »fih)|-v , . H W ii 'v-es per

year .

The Mure value is unknown.

At the end of ten yea rs , the fu tu re va lue of Pe te 's

accoun t is $73 6 2 4 . 9 0 .

b ) T h e fu ture va lue of Pe te ' s i nves tmen t is h igher than

Dee ' s i nves tmen t b e c a u s e e a c h depos i t Pete m a d e had

more t ime to a c c u m u l a t e in terest , a n d add i t iona l in terest

w a s paid on the a c c o m u l a t e d in terest ,

12 . T r e y : T h e regu lar p a y m e n t a m o u n t is $600 .

T h e p a y m e n t f r equency is quar te r ly or 4 t imes per year.


T h e p a y m e n t s a re m a d e at the end of e a c h p a y m e n t

per iod .


T h e c o m p o u n d i n g f r equency is quar ter ly or 4 t imes per

year .


At the e n d of two yea rs , the fu tu re va lue of T rey ' s

accoun t is $ 4 9 5 3 . 9 5 ,

S a m : T h e regu lar p a y m e n t a m o u n t is $ 2 4 0 0 ,

T h e p a y m e n t f r equency is annua l , or once per year .


T h e p a y m e n t s a re m a d e at the end of each p a y m e n t

per iod . T h e annua l in terest rate is 3 .8%, T h e c o m p o u n d i n g f r equency is annua l , or once per year .

The future value Is unknown.

At the end of t w o yea rs , the fu ture va lue of S a m ' s

accoun t is $ 4 8 9 T 2 0 ,

D i f fe rence : 4 9 5 3 , 9 5 , - 4 8 9 T 2 0 = 62 .75

T rey ' s i nves tmen t is wo r th $ 6 2 . 7 5 m o r e than S a m ' s

inves tment .

13. To ta l pr ice of en te r ta inmen t s y s t e m :

( 2 4 9 9 ) { T 1 3 ) = 2823 .87

T h e regu lar p a y m e n t a m o u n t is $ 2 2 5 .

T h e p a y m e n t f requency is month ly , or 12 t imes per year .


T h e p a y m e n t s are m a d e at the end of each p a y m e n t

per iod .


T h e c o m p o u n d i n g f r equency is month ly , or 12 t imes per

year. The future value is unknown.

In one year . M igue l ' s a c c o u n t wi l l be wor th $2745 .00 .

$ 2 7 4 5 . 0 0 - $2823 .87 = - $78 .87

Migue l wi l l be shor t $78 .87 .

14. a) J i l l : The regular payment amount is

unknown. T h e p a y m e n t f r equency is month ly , or 12 t imes per

year .

T h e n u m b e r of p a y m e n t s is 360 .

T h e p a y m e n t s a re m a d e at the e n d of each

p a y m e n t pe r iod .

T h e annua l in terest rate lo ' - l " - - .


t imes per year .

T h e fu tu re va lue is $ 2 5 0 000 .

Jill needs to invest $189 29 at the e n d of each

mon th

$ 1 8 9 . 2 9 - 3 6 0 = 168 144.40

V a u g h n : The regular payment amount is

unknown. T h e p a y m e n t f r equency is month ly , or 12 t imes per

year .


T h e p a y m e n t s are m a d e at the end of each



T h e c o m p o u n d i n g f requency is month ly , or 12

t imes per year .

T h e fu tu re va lue is $ 2 5 0 000

V a u g h n needs to invest $78 .16 at the end of e a c h

mon th

$73 00 0 = 28 137.60

$6.1 ' ''A .10 - $28 137.60 = $40 006 .80

Jill I , e< i , to invest $40 006 .80 more than V a u g h n

ov> ' loe 3 0 years .

b) , ^.o' regu lar p a y m e n t a m o u n t is $189 .29 ,

T h e p a y m e n t f r equency is month ly , or 12 t imes per

year .



p a y m e n t per iod .



t imes per year .


V a u g h n wi l l have $ 6 0 5 501 .19 at the e n d of

30 years

15. T h e regu lar p a y m e n t a m o u n t is $300 .

T h e p a y m e n t f r equency is week ly , or 52 t imes per

year .





T h e c o m p o u n d i n g f requency is week ly , or 52 t imes

per year .


T i m wi l l have $34 679 .08 at the end of two yea rs .

Wi th the $ 5 0 000 he ge ts f r om sel l ing his f irst

sa i lboat , he has $84 679 .08 .

D i f fe rence : 120 000 - 84 679 .08 = 35 320 .92

T i m wi l l not have e n o u g h m o n e y to buy his d r e a m

sai lboat . He needs an addi t iona l $35 320 .92 . a s s u m i n g

the sa i lboat 's pnce has not inc reased in the two yea rs .

1-18 C h a p t e i 1- h m a n c i a l M a t h e m a t i c s : Inves t ing Money

16. a)

S imi la r

Both have a tota l pr inc ipal of $ 1 2 0 0 .

Both ea rn 6 % annua l in terest

c o m p o u n d e d month ly .

B ^ l i a r e inves ted for 10 years .

Different

Opt ion A IS a

s ing le depos i t

wh i le opt ion B

is a ser ies of

paymen ts .

b)

Olio p,-. i -o |_ (

per A n n u m

O p f j o ^ i A _ _ I C jp t ioo B I

1 o ' ' ' f i - ' i u i . • a n . i i l l ^H'< ri'.)u.l> "

.f r' s

i iOi.-n

; ' o ; O .

1 -o 0 /

S40 n ,3^

/'g 29

I l o i a / g ^

25(

investment A

investment B

i t l J

f.S . I t

T ime 1 J-.'l-'j-i o f hiVt=,..:)tiorif (.;>,

t iptpo O p t : o r i B f' 1200 0

2 — p i ; .92 ' i 9 204 t2 4~" - L j t ) 24 'i'.r 349 0 3

6 - 4

1 / 1 9 40 301^09

1930 97 ^ " ~ 1323 2 9 " 10 '.-'I/O' 23^'^ " l b 1 8 7o

1 he v a l u e of ( )p t ion tJ g rows rnuoi i taster than the va lue

of Opt ion A, but m u c h of Opt ion B's g rowth is due to the

mon th l y depos i ts . Opt ion A ea rns more interest than

opt ion B over the 10 years .

17 . No . e.g. , T h e probabi l i ty that his t ips wi l l equa l the

s a m e a m o u n t each mon th is very unl ikely. (However , the

p rob lem cou ld be so lved us ing the fo rmu la A = R+R(1+ if + R(1 + if + ... + + , |n^1 and

chang ing R to the va lue Farah depos i ts each mon th . )

18. A m o u n t n e e d e d : 5000 - 5000 (0 .25 ) = 3750

Farah wi l l need $ 3 7 5 0 in her accoun t af ter two years .

The regular payment amount is unknown.

T h e p a y m e n t f r equency is month ly , or 12 t imes per year

T h e n u m b e r of paymen ts is 24 .

The p a y m e n t s a re m a d e at the end o f each paymen t per iod .



t imes per year .



Fa rah needs to depos i t $ 1 5 0 . 9 3 at the end of e a c h m o n t h in o rder to buy a new c o m p u t e r in two yea rs .

1 i . R e g u l a r p a y m e n t i n v e s t m e n t : T h e regu lar p a y m e n t a m o u n t is $50 .

T h e p a y m e n t f r equency is s e m i - a n n o a l . or 2 t imes per year.

T h e n u m b e r of p a y m e n t s is 4 0 .




T h e c o m p o u n d i n g f r equency is sem i -annua l , or 2

t imes per year .


T h e va lue of the accoun t a f ter 20 yea rs is $3370 .13 .

L u m p s u m i n v e s t m e n t : T h e pnnc ipa i is $3370 .13 .

T h e annua l in terest rate is 5%,

T h e c o m p o u n d i n g per iod is semi^annoaL or 2

t imes per year .



T h e fu ture va lue of the i nves tmen t is $53 365 .38

T h e final va lue of the inves tment is $5522 .35 .

2©. A m o u n t n e e d e d : 4 6 000 (1 .05 ) ^ 4 0 0 0 = 4 4 300

T h e regu lar p a y m e n t a m o u n t is $550 .

T h e p a y m e n t f r eguency is month ly , or 12 t imes per

year .

T h e n u m b e r o f p a y m e n t s is 60 .

T h e p a y m e n t s a re m a d e at the end o f each

p a y m e n t per iod .

T h e annua l in terest rate is 9 ,8%.


t imes per year .


In f ive years . Pat 's accoun t wi l l be wor th

$42 3 6 6 . 0 1 , Pat needs to save $44 300 to a f fo rd

the car, so he canno t m a k e the pu rchase Pat wi l l be shor t by $1933 ,99 ,

F o y n d a t i o n s o f M a t h e m a t i c s 12 S o l y t i o n s M a n u a l 1-19

M a t h i n A c t i o n , p a g e 5S . e .g . . the in terest rate for a 5^year G I C is 1 .267% per a n n u m , and the in terest rate for a 5-year mor tgage is

5 . 1 9 % , c o m p o u n d e d semi -annua l l y . . T h e fu tu re va lue of the i nves tmen t is $54 2 3 0 . 3 8 6 . . . or

$54 230 .39 , a n d the interest e a r n e d is $ 4 2 3 0 . 3 9 .

. T h e fu tu re va lue of the mo r t gage (wi th no regular loan

p a y m e n t s ) is $64 5 9 9 , 9 1 7 . . . or $64 599 9 2 . and the

in terest c h a r g e d is $14 599 ,92 ,

. T h e d i f fe rence b e t w e e n the in terest pa id by the bank

and the in terest e a r n e d by the bank is $10 369 ,53 . w h i c h

represen ts the a m o u n t ea rned by the bank ,

. T h e g rea te r the d i f fe rence be tween the a m o u n t of

in terest that a bank pays on an inves tmen t and the

a m o u n t of in terest that t he bank cha rges on a loan , the

m o r e m o n e y the bank wi l l m a k e .

L e s s o n 1 .6 : S o l v i n g I n v e s t m e n t P o r t f o l i o

P r o b l e m s , p a g e 6 4

1. a) A G I C w o u l d a l low S tan to ea rn in terest on the $300

he has f r o m his s u m m e r job . T h e h igh interest sav ings

accoun t w o u l d a l low h im to ea rn interest on his w e e k l y

sav ings .

b) G I C : T h e pnnc ipa i is $300 .


T h e c o m p o u n d i n g p e n o d is annua l , or once per year .

T h e t e r m (in yea rs ) is 1 year .


T h e GIC wi l l be wo r th $ 3 1 5 at the end of o n e year .

S a v i n g s a c c o u n t : T h e regu lar p a y m e n t a m o u n t is $15 .

T h e p a y m e n t f requency is week l y , or 52 t imes per year .


T h e p a y m e n t s a re m a d e at the end of e a c h p a y m e n t per iod .


T h e c o m p o u n d i n g f r equency is week ly , or 52 t imes per year .


T h e sav ings accoun t wi l l be wor th $791 .20 at the end of one

year.

To ta l s a v e d : 315 + 791 .20 = 1106 20

D i f fe rence : 1750 1106.20 = 643 .80

S tan wi l l not have e n o u g h m o n e y in o n e year to buy the

gui tar . He n e e d s $ 6 4 3 . 8 0 more .


T h e p a y m e n t f r equency is week l y , or 52 t imes per year . T h e n u m b e r of p a y m e n t s is 52 .

T h e p a y m e n t s are m a d e at the end of each p a y m e n t p e n o d .


T h e c o m p o u n d i n g f requency is week l y , or 52 t imes per year ,

S tan needs to depos i t $27 .21 into his accoun t each w e e k to

mee t his goa l .

2 I n v e s t m e n t a c c o u n t : T h e regular p a y m e n t a m o u n t is $50 .

T h e p a y m e n t f r equency is week l y , or 52 t imes per year .


T h e p a y m e n t s a re m a d e at the e n d of e a c h p a y m e n t per iod .


T h e c o m p o u n d i n g f requency is week ly , or 52 t imes per year .

Ttie future value is unknown. T h e sav ings accoun t wi l l be wo r th $5416 .92 at the end of two

DWerence : 10 000 - 5416 .92 = 4 5 8 3 , 0 8 Rob in and Les l ie need an add i t iona l $4583 .08 in t w o years .

C S B : I tir imncipul o. !inkn.'wt<

I l ie on iu io l iot<.'io;,l mto- r- (7'.,

f h e . .o i i i pound ing penod ••- - •noool , nr on'X- p.a y.>at

I l u ! t ( 'nn (in yoors ) m 2 years

I h u l u h i i u vo'i.io IO $4 .33 . i 0 ; t

; >r,biii and I frslie s pau ' t t h . -,l-'Olld (Jivi: tp.-ir. $4(143 h'

3. C S B s

Y e a r Z Z Z J n A ( $ )

1 1000 0,0.^.4 1 , i31

y l o o o f) 0 3 1 130t,

,) ,)0 0 9 3 4 _ 0 1263

4 Tooo 6 0 3 4 j _ 1222

5 1000 3- 0 f l , \v.\\

t) 0 0 0,034 1 ^ m a

/ 00 ' 3 .Ua4 ' 119' . !

8 100(^ 0 034 ior,;! '

9 ^ h i O l 0 (TA I Z Z l l Z Z Z I Z I l l l 100C i P 034 " " i " 1000

, _ _ _ p o ' 7

I he c3;>Bs a i e w n h h $1 n / 7 4-:

T r u s t a c c o u n t . Tno pr inc ipal is $oOOO.


T h e c o m p o u n d i n g p e n o d is quar tedy , or 4 t imes per

year.

T h e te rm (in yea rs ) is 42 yea rs .


T h e trust accoun t is w o r t h $18 083 .03 .

G I C : T h e pnnc ipa i is $10 000

T h e annua l in terest rate is 3 .95%. T h e c o m p o u n d i n g penod is sem i -annua l , or 2 t imes per

ygar.



The GIC is wor th $14 786 .80 .

To ta l : 11 677 .32 + 18 083 .03 + 14786 .80 = 44 5 4 7 . 1 5

F i v e - y e a r b o n d : T h e pnnc ipa i is $44 547 .15


T h e c o m p o u n d i n g penod is annua l , or o n c e per year .

T h e te rm (in years ) is 5 yea rs .


T h e f i ve-year bond wi l l be wor th $57 125.96 .

4. a) I n v e s t m e n t a c c o u n t : T h e regu lar p a y m e n t a m o u n t

is $50 . T h e p a y m e n t f r equency is month ly , or 12 t imes per year .

T h e n u m b e r of p a y m e n t s is 36 . T h e p a y m e n t s are m a d e at the end of each p a y m e n t

per iod . T h e annua l interest rate is 2 . 7 % . T h e c o m p o u n d i n g f r equency is month ly , or 12 t imes per

year .


T h e inves tment accoun t is wo r th $1872 .72 .

R E S P a c c o u n t : T h e regu lar p a y m e n t a m o u n t is $ 1 0 .

T h e paymen t f r equency is month ly , or 12 t imes per year .

T h e n u m b e r of p a y m e n t s is 216 . T h e p a y m e n t s are m a d e at the end of each p a y m e n t

per iod. T h e annua l interest rate is 3 .2%.


T h e cofTipouncling f requency is month ly , or 12 t imes per year .

The future value is unknown

T h e R E S P accoun t is wor th $2915 .79 .

To ta l ; 1872 .72 + 2915 .79 = 4788 .51

Pau la has $4788 .51 w h e n she star ts f i rst year .

b ) D i f fe rence : 4788 .51 ^ 2 0 0 0 = 2788 .51

T h e pr inc ipal is $2788 .51

T h e annua l mterest rate is 3 ,5%,

T h e c o m p o u n d i n g penod is dai ly, or 365 t imes per year T h e te rm (in years ) is 1 year . The future value is unknown.

T h e sav ings accoun t is wor th $ 2 8 8 7 . 8 3 af ter o n e year.

Pau la wil l have e n o u g h m o n e y saved for second year c| D i f fe rence : 2887 83 ^ 2000 = 887 83

T h e pr inc ipal is $887 83

T h e annua l interest rate is 3 ,5%.

T h e c o m p o u n d i n g penod is dai ly , or 365 t imes per year

T h e te rm (in years ) is 1 year.


T h e sav ings accoun t is wor th $919 45 af ter one year .

A m o u n t shor t : 2 0 0 0 - 919 .45 = 1080 55

Pau la wil l not have enough m o n e y saved for th i rd year

S h e needs to save $1080 .55 over the s u m m e r .

5. a) Gay la ' s pr inc ipa l : (15) (12) (12) = 2160 C o r e y pnnc ipa i : (18) (12) (10) = 2160 T h e y both inves ted $2160 .

b | Gay la has the greater sav ings because her m o n e y has been inves ted for 12 years longer than Corey ' s money .

G a y l a : R e g u l a r p a y m e n t inves tment :

lie regular p a y m e n t a m o u n t is $15 .

T h e p a y m e n t f r equency is month ly , or 12 t imes per year n u m b e r of paymen ts is 144.

T h e p a y m e n t s are m a d e at the end of each p a y m e n t per iod

annua l interest rate is 3 .6%.

T h e c o m p o u n d i n g f reguency is month ly , or 12 t imes per

year .


T h e inves tment is wor th $2696 .70 .

L u m p s u m i n v e s t m e n t : The pnnc ipa i is $2696 70 T h e annua l in terest rate is 3 .8%. T h e c o m p o u n d i n g per iod month ly , or 12 t imes per year T h e te rm (in years ) is 10 year.


Gay le 's tota l inves tment is wor th $3940 .97 .

C o r e y : T h e regular paymen t a m o u n t is $18 .

T h e p a y m e n t f reguency is month ly , or 12 t imes per year . T h e n u m b e r of paymen ts is 120.


per iod .


T h e c o m p o u n d i n g f requency is month ly , or 12 t imes per

year .


Corey ' s i nves tmen t is wor th $2622 .73 ,

Gay le has a larger inves tment than Corey ,

4 < 4 C ' 3- 0 I I't'- '• I

i iO-:•(-•-• (f-'cr,- -.1 i

I ••• ' HI p< .1 'I •< , | r« ; [ II >i I- • I

il a l , o r 2 t imes per

1 yea rs ) is 10

f a /oe is unknc ,v -.n- , o , 0 ,

4 S B - .

•Of 1 I

F (Sj

iO! 0

1 . i

. O o m

n : A IS} S 1 ",}• I f

1 h ; o o

1 . i

. O o m 1 - • ' " " •

: : ; 2 f ' i ! > /

1 3 1000 [ 0 , 0 4 8 1 , s ; y 1 f: • I.OOM 3 , ' 3 : ;

t :» i 1

'OOO ! o i j - ' o j

I 1 1 1 ; o 4 ' j o o

The C S B ; i a re wo r th ! i ' / O S • ~ *— —

d.-f p.syaK o t io os tment : The (I p,'./(( a m o u n t is ; t S O ; ,

' ' , 1 . ' ' • "1 . / . ; • , ' . I i ce per year ,

'ach p a y m e n t

or once per year .

I ne annua l in terest rate is 5%. '• ' • • I'Ti ':•>•'. Ol, { .• v-.i,':: , ,

" ' ! . • ' • w 4, / ! I i-.-:-.>:-v,,,

' I H". '. l iof [,• . , J./ Of. ' , , / 0-3.

L y . t i p s y m i n v e s t m e n t : 1 ne pr inc ipal is $16 532 98 T h e annua l in terest rate is 5%.

T h e c o m p o u n d i n g per iod is a n n u a l , or once per year T h e te rm (in yea rs ) is 20 years .


T h e trust accoun t is wo r th $ 4 3 8 6 6 . 9 1 .

To ta l ; 15 453 .18 + 5758 ,14 + 4 3 866 .91 = 65 078 .23 Jayne ' s i nves tment por t fo l io is wor th $65 078 23

Pr inc ipa l : 10 000 + 1000(5 ) + 500 (20 ) = 25 000 Interest ; 65 078 .23 - 25 000 = 4 0 078 .23

Rate of re turn = i i O Z 8 : 2 3 2 5 000

Rate of return = 1 603 , .

Jayne ' s rate o f return on her i nves tment is 160 .3%.

7. a) S a v i n g s a c c o u n t : T h e regu lar p a y m e n t a m o u n t is $50 .

T h e p a y m e n t f r equency is mon th ly , or 12 t imes per

year.


T h e p a y m e n t s a re m a d e at the end of each paymen t

penod .

T h e annua l in terest rate is 2 . 7%.

T h e c o m p o u n d i n g f requency is month ly , or 12 t imes

per year.


W h e n Ela is for ty, the sav ings accoun t is wor th $15 888 .14 . F i r s t 10 -year G I C : T h e pnnc ipa i is $15 888 .14 T h e annua l in terest rate is 4 . 2 % .

T h e c o m p o u n d i n g p e n o d is month ly , or 12 t imes per year .

T h e te rm (in years ) is 10 years . The future value is unknown.

W h e n Ela is f i f ty, the G I C is wor th $24 163.41

F o u n d a t i o n s of Mathemat ics 12 S o l u t i o n s Manual 1-21

S e c o n d 1 © - f e a r G I C : T h e pr inc ipa l is $24 1 6 3 . 4 T

T h e annua l in terest rate is 4 . 3 % . T h e c o m p o u n d i n g per iod is mon th l y , or 12 t imes per

vear .

! h'> It.'on o n y o . i r o i;. K ) y u o r - .

llu- iiituii- v.ihir unktumu

y V l i c u 1 i l i-. ^.i^3y, I ho t 4 i ; is wt ; r t l i $ ' / i 13 t}5.

F i r s t 1 0 - y e a r b o i i d : I h t ; p n o f i p n l is $500 .

I h i ; Honn . i l intun,"..! l o l u is 3 PrX,

1 p.: . .u iupDuodi iKi o-Hind i s a n n u a l , or once per year .

! h t ' l»?ini (10 y t j . i i s ) r. 10 y r a r s

ill. - litUut: \/uH:n i ; iniknrmn

y'4 i f ;n r i a I- fifiv, t in- t i ond v. wr j f l l i $733 .04 .

S e c o n d lO^yeor b o n d : 1 l u ; onnc ipa l is $733 .04 .

; he . lon i i . i l in1c>o-,t l o l i : IS 3 ' } '3 -

1 h f ' .offii.rtiund 'Hq p i s ' f K l r. o n u u a i , or once per year .

; h; i<H,,! (!fi v^Nir .) IS y o o r o

; h' in: I ire value is unknown.

y y h i . n i i a is s ixty, the b o n d is wor th $1074 .69 .

U.lti I 116.85 + 1 0 7 4 . 6 9 = 3 8 1 9 1 . 5 4

W h e n Ela t u m s sixty, the to ta l value of his port fo l io is

$38 191 54 .

h) Pr inc ipa l : 50 (240 ) + 50 ' > T sOO

Interest : 38 191.54 12 500 - ' 3 691 .54

25 691.6-1 - 4e of re turn

r o s e of return = 2 .055 . . . s rate or return on his i nves tmen t is 2 0 5 . 5 % .

8. a) Cos t of tnp : 2 0 0 0 + 3 0 0 ( 1 2 ) = 5600


T h e annua l in terest rate is 5%o.

T h e c o m p o u n d i n g p e n o d is a n n u a l , or o n c e per year .

T h e te rm (in yea rs ) is 4 y e a r s .


T h e G I C is wor th $1458 .61 a t maturi ty.

D i f fe rence : 5600 ^ 1458.61 = 4141,39

No , Jo wi l l not have e n o u g h m o n e y for her tnp in four

years . S h e wi l l be $ 4 1 4 1 . 3 9 shor t ,

b) If she m a k e s w e e k l y depos i t s for four years , that is

2 0 8 depos i t s . D iv ide the a m o u n t s h e needs to have by

208 .

4141 .39

208 - = 19.910.

e .g . , I es t ima te that J o wi l l n e e d to m a k e depos i t s of an

a m o u n t less than $19 91 to mee t her goa l .


T h e p a y m e n t f r eguency is w e e k l y , or 52 t imes per year .


T h e p a y m e n t s a re m a d e at t h e end of each p a y m e n t

per iod . T h e annua l in terest rate is 2 . 3 % . T h e c o m p o u n d i n g f r e q u e n c y is week ly , or 52 t imes per

year. T h e fu ture va lue is $ 4 1 4 1 . 3 9 .

Jo needs to m a k e w e e k l y depos i t s of $19 .01 to mee t her

goa l .

9. Opt ion A : G I C : T h e pr inc ipa l is $15 000 .

T h e annua l in terest rate is 4 . 1 % . T h e c o m p o u n d i n g per iod is annua l , or once per year .



The GIC IS wo r th $22 4 18 09 .

S a v i n g s a c c o u n t : T h e pnne ipa l is $ 3 6 3 8 .


T h e c o m p o u n d i n g p e n o d is week l y , or 52 t imes per

y s 3 r



T h e sav ings accoun t is wo r th $ 5 3 7 2 . 4 7 .

To ta l : 22 4 1 8 . 0 9 + 5372 .47 = 27 792 .04

Op t ion A wi l l be wo r th $27 790 .56 in ten yea rs .

Opt ion B : T h e pnneipa l is $18 6 3 8 .


T h e c o m p o u n d i n g p e n o d is dai ly , o r 365 t imes per

ygar.



Opt ion B wi l l be wo r th $27 527 .39 in ten yea rs .

Opt ion A is wo r th $263 .17 more t han op t ion B.

Derek shou ld c h o s e opt ion A.

10. e .g . . A n inves tmen t por t fo l io m a y cons is t of

s ing le p a y m e n t i nves tmen ts or regular p a y m e n t

i nves tmen ts . S o m e inves tmen ts m a y lock in funds

for a per iod of t ime l imi t ing a c c e s s to it but o f ten

of fer a h igher in terest ra te . Inves tments o f fenng a

lower in terest rate usua l ly a l low access to the

f unds . A h igher i nves tment a m o u n t usua l ly t ends

to of fer h igher in terest ra tes. T h e g rea te r the

pnnc ipa i , t e r m , in terest rate, and c o m p o u n d i n g

f requency , the fas ter the i nves tmen t wi l l g row .

1 1 . 3 ) Bet ty has $200 000 now. so th is is the

p resen t va lue . S h e wil l have no m o n e y in the

accoun t in ten yea rs , so the fu ture va lue is ze ro .

So lve for the regu lar p a y m e n t amoun t .


T h e present va lue is $200 000 .

T h e p a y m e n t f r equency is month ly , or 12 t imes per

yggf T h e n u m b e r of p a y m e n t s is 120.





t imes per year .

T h e future va lue is 0.


Bet ty wi l l rece ive 120 month ly p a y m e n t s of

$ 2 1 2 1 . 3 1 . b) The regular payment amount is unknown.

T h e p resen t va lue is $200 000 . T h e p a y m e n t f r equency is month ly , or 12 t imes per

year


T h e p a y m e n t s are m a d e at the end of e a c h



T h e c o m p o u n d i n g f r eguency is month ly , or 12

t imes per year .

T h e fu ture va lue is 0.


I used the f inanc ia l app l ica t ion on my ca lcy la tor ; Bet ty w o u l d rece ive 120 month ly p a y m e n t s of $ 2 3 7 4 , 0 4 if the interest rate inc reased to 7 ,5%.

12 . R e g u l a r p a y m e n t i n v e s t m e n t : T h e regu lar p a y m e n t a m o u n t is $150 ,

T h e p a y m e n t f r equency is annua l , or once per year . T h e n u m b e r of paymen ts is 50 .

T h e paymen ts are m a d e at the end of e a c h p a y m e n t

per iod.


T h e c o m p o u n d i n g f requency is annua l , or once per year .

Tfie future value is unknown.

T h e inves tment is wor 320,88,

M o n t h l y I n c o m e : The regular payment amount is

unknown.

T h e present va lue is $113 920 ,88 ,

T h e paymen t f requency is month ly , or 12 t imes per year . T h e n u m b e r of paymen ts is 120, T h e paymen ts are m a d e at the end of each p a y m e n t per iod .

T h e annua l in terest rate is 4 , 8 % .

T h e c o m p o u n d i n g f requency is month ly , or 12 t imes per year .

T h e fu ture va lue is 0.

I used the f inanc ia l app l ica t ion on my calcu lator : S ty ' s g randmo the r wil l rece ive 120 mon th l y p a y m e n t s of

$1197 .20 . She wil l rece ive $143 664 .00 a l toge ther in paymen ts .

C h a p t e r S e l f - T e s t , p a g e 6 8

1 -S' r> • 6

f h e i .nvo^ir i , - . . ! wi l l doub le in abou t 12 yea rs

T h e pr inc ipal is $40 000 .

T h e annua l in terest rate is 633.

T h e c o m p o u n d i n g per iod is annua l , or o n c e per year. The term (in years) is unknown. T h e fu ture va lue is $80 000 .

I used the f inancia l app l ica t ion on m y ca lcu la tor ; Hal 's inves tment wil l doub le in 11.9 years b}A = P + Prt

A is $80 000 ; P is $40 000 ; ris 6 % or 0.06 80 000 = 4 0 000 + (40 000) (0 .06) ( f ) 4 0 000 = 2400 f t= 16 .666 . . .

W i th s imp le interest, Hal 's i nves tmen t wi l i doub le in 16.67 years .

2 . O p t i o n A : T h e pr inc ipal i 3 i 3 900 .

T h e annua l interest rate is 6%.

T h e c o m p o u n d i n g per iod is sem i -annua l , o r 2 t imes per

The term (in years) is unknown. T h e fu ture va lue is $50 000 .

I used the f inanc ia l app l ica t ion on my calcu lator ; The

opt ion A inves tment wil l g row to $50 000 in 48 .28 per iods

or 24 .14 years .

O p t i o n B : The pr inc ipal is $12 000 ,

T h e annua l interest rate is 5 , 1 % .

T h e c o m p o u n d i n g per iod is quar ter ty , or 4 t imes per year .

Tf ie term (in years) is unknown. T h e fu tu re va lue is $50 000 ,

I used the f inanc ia l app l ica t ion on m y ca lcy la tor ;

T h e op t ion B i nves tmen t wil l g row to $50 000 in 112.64 per iods or 28 .16 years .

Va l shou ld c h o o s e op t ion A because she wi l l reach her f inanc ia l goa l abou t 4 years sooner .

3 ."4 I ! . , „ , • 0/ O'p.l ( . . }

• •' • , ' ». , •( f! 3 O'O' <

' o it oi . i ,1 p . i v ( i i« ' (H .j!u I i-ii : yo ,

' r n''n= - c j .n ar v' ' ^ < !'»n!--i,-, or 12 t imes per

iber of p a y m e n t s is 2 4 0 ,

Tients a re m a d e at the end of each .,.... . p e r i o d ,

annua l in terest rate is 5 .8%.

T h e e o m p o u n d i n g f reguency is month ly , or 12

t imes per year .


W a r r e n ' s i nves tmen t is cur rent ly wor th $2256 .24

Interest ; 2 2 5 6 . 2 4 ^ 1200 = 1056,24

Rate of re turn = 1 0 5 6 2 4

1200,00 Rate of return = 0 .880 , , , W a r r e n ' s rate of return on his i nves tmen t is 8 8 % . b | W a r r e n inves ted a tota l ., ; /• i< - ' t ie m a d e mon th l y depos i t s for f ive years , e a c h depos i t v^ould be:

(5)(12)

regular p a y m e n t a m o u n t is $20 .

T h e p a y m e n t f r equency is month ly , or 12 t imes per year.

T h e n u m b e r o f p a y m e n t s is 60 ,

T h e p a y m e n t s a re m a d e at the end of each p a y m e n t p e n o d .



t imes per year .


W a r r e n ' s i nves tmen t w o u l d be current ly wor th $1388 .25 .

c| The regular payment amount is unknown.

T h e p a y m e n t f r equency is month ly , or 12 t imes per year





T h e e o m p o u n d i n g f reguency is month ly , or 12

t imes per year .

T h e fu tu re va lue is $2256 .24 .

I used the f inanc ia l app l ica t ion on m y calcu lator : W a r r e n w o u l d have n e e d e d to m a k e month ly p a y m e n t s of $32 .50 .

4 . a) A l e x : G I C : T h e pnnc ipa i is $ 5 0 0 0 .



F o u n d a t i o n s of Ma themat ics 1? S o l u t i o n s Manual 1-23

• l l , - I c i r . i f i . i \ii .1? , | i< ' } v ' - ' i ' ' -

I III- Itlt'lli K/.iliH- i:, >Ulkll()Wn

I t|.> < 4 i . I-. W u . l l l .<l>

C S B - |»n!i; iM-il r. $'/fH)iJ

I t w rinu.it i n t . - ! c s l r.itt- is i 1

s t i « - . { . i . i p u u i i . j m c j f f i s ' - t i I' ; . . - n i i , i . ; i n i . i l , or 2 t imes per

yf>,lf

I p r !<ir(i OM ys- H ' I J y^ 'Uts

; / } . . f,,lh(t' Wih.f i: lirih'H nvi!

Its.- i . S B IS w u U h $-0^'f,1 PH',

S a v i n g s a r c o i i r i t . 1 fi»- i s t i u l o . ' o . i yme i i t a m o u n t is $15 .

11, . - 0 . 0 / 0 . ' I'.: i:* oo.;ii< / IS w c r P l y o i o t imes per year .

I :,<" . l O O i i . J f u ; | » . i . / ' i i . - ! ; l s r / O f -

o , . . , , , . y . p s - . . - .",!" . s . i p . . ..i l o u 'I eac t i p a y m e n t

p e r i o d . ' T h e annua l in terest rate is 1.4%. T h e c o m p o u n d i n g f requency is week l y , or 52 t imes per

year .


T h e accoun t is wo r th $ 4 0 3 9 . 1 8 .

To ta l ; 6 2 9 9 . 3 6 + 2 2 6 1 . 8 8 + 4 0 3 9 . 1 8 = 12 600 .42

T h e total va lue of A lex ' s port fo l io is $12 600 .42 .

' amie : B o n d : A = P(1 + rt)

$ 3 0 0 0 ; f is 2 . 7 % or 0 .027 ; t is 9

3000(1 + (0 .027) (9) )

3729

I he bond is w o r t h $ 3 7 2 9 .

C S 3 : T h e pr inc ipa l is $700 .

• annua l in terest rate is 2 .8%,

4if5 c o m p o u n d i n g per iod is sem i -annua l , or 2 t imes per

year .



T h e C S B is wo r th $760 .90 ,

S a v i n g s a c c o u n t : T h e regu lar p a y m e n t a m o u n t is $ 1 0 0 .

T h e p a y m e n t f r equency is month ly , or 12 t imes per year .

T h e n u m b e r of p a y m e n t s is 72 . T h e p a y m e n t s a re m a d e at the end of e a c h p a y m e n t

penod . T h e annua l in terest rate is 1,7%, T h e c o m p o u n d i n g f r equency is month ly , or 12 t imes per


T h e accoun t is wo r th $7574 ,37 .

Tota l - 3729 + 760 .90 + 7574 .37 = 12 064 .27

T h e total va lue of Jamie ' s port fo l io is $12 064 .27 .

b) A l e x :

Pr inc ipa l ; 5000 + 2000 + 15(52) (5) = 10 900

Interest ; 12 600 .42 ^ 10 900 = 1700.42

1700.42 Rate of re turn

Rate of return = 0 .156 . . . A lex ' s rate of return on his inves tment is 15 .6%.

P r ^ d p a l ; 3000 + 700 + 100(12) (6 ) = 10 900

Interest ; 12 064 .27 - 10 900 = 1164 .27

1164.27

R a t e o f r e t u n . - ^ - ^

Rate of return = 0 .1068 . ..

Jamie ' s rate of return o n her inves tment is 10 .7%.

A lex has a grea te r rate of re turn on his por t fo l io

t han Jam ie d o e s .

C h a p t e r R e v i e w , p a y e 7 1

1. a) A = P + Prt

A is $ 2 8 5 0 ; P i s $ 1 5 0 0 ; r i s 6

2850 = 1500 + (1500) ( r j (6 )

1350=OOOOr

f = 0 , 1 5

T h e C S B ea rned an annua l in terest rate of 1 5 % ,

b) T n s h w o u l d get $ 2 8 5 0 , T h e in terest is pa id

annua l l y so the a m o u n t wi l l be the s a m e w h e t h e r

she r e d e e m s the C S B w h e n she is 18 or 18 and a

halt

2.JO

V : i n c lf,.Aj%f Z

! i 4 ( ; ! o s l ! labs p s .

/ \ O U U I i _ J_

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1 r

I ~* i 11 1

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C 4 B i S v L 4 h 3 l : 3 / 4

b)

G I C

10 000

o o n '

C S B

7 ( 4 1 0

0.114

i o 0 iO (!{• , / / n o , o o

: 1 ; i 9 0 UP ; o ; 4 ) i fK»

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I V S N I U .3 Oi ' o o u o u t h e

Comparisons of Investments

18 One

16 ono

2 14C'L''J

1 12 0SU

2 10 000

i n. -0

3 s 000

1 uon

2 000

e

G r a n d m o t h e r ' s

G I C

G r a n d f a t h e r s

CSB

5 6 Years

T ime V a l u e of Inves tment ($) ^

l y n a i b i G IC j : S B ^

1 10 630 ,00 7798.00

~3 11 890 .00 9 3 9 4 00

" 5 " 13 150,00 • .0.00

~ 7 00 6 .00

15 670 ,00 2 00

1 1 16 930 .00 15 778 00

lo " " 18 190.00 17 374 .00

1-24 C h a p t e r 1 l - i o a n c i a l M a t h e m a t i c s : I n v e s t i n g M o n e y

re in terest is inc reas ing in

T h e C S B wil l soon be wo r th 894.71

' • * "" • ' • ••' ••Oil have the g rea tes t re turn

' - f . ' - ' S imp le interest i nves tmen ts • • • ' m p o u n d interest i nves tmen ts

over a shor t t ime. 1-9 S o t O . J / : f • )

' • • • ' • 4 6 2 ; f ! s 5 , i i l l ! . , « • . • . , . . ( , ' , . . ..

1r * ' j 4 . = F f l + f )"

r = 5 . 3 % c o m p o u n d e d month ly

116. . . ; f = S y e a r s . 11 = 60 - 1 + 0.0 - M ' . f °

34

605 34 ^ 2000 = 605 .34

Rate of r e t u m = 2000 00

Rate of re turn = 0 .3026 . . .

T ren t ' s rate of r e t u m is 3 0 . 3 % .

Son ia has a s l ight ly h igher rate of return than Tren t d o e s

c | S o m a ' s inves tment ea rned more interest b e c a u s e the

annua l in terest rate w a s h igher and the te rm w a s too

shor t for the c o m p o u n d i n g of interest in T ren t ' s accoun t

to be no t i ceab le .

4 . a) J o h n n y wil l ea rn more interest because the in terest

on his accoun t is c o m p o u n d e d more f requent ly

J a m e s : T h e pr inc ipal is $2000 .

T h e annua l mterest rate is 7 .4%.

T h e c o m p o u n d i n g per iod is sem i -annua l , or 2 t imes per year .

f f t e rm (in years ) is 5 years .


J a m e s ' s inves tment is wor th $2876 .19 .

Interest ; 2 8 7 6 . 1 9 - 2000 = 876 .19

J a m e s ea rned $876 .19 in interest ,

J o h n n y : T h e pnnc ipa i is $2000 .


T h e c o m p o u n d i n g penod is week ly , or 52 t imes per year The te rm (in years ) is 5 years .


Johnny ' s i nves tment is wor th $ 2 8 9 4 71

Interest ; 2894 .71 ^ 2000 = 894 .71

J o h n n y ea rned $894 .71 in interest .

Johnny ' s i nves tment ea rned more interest than J a m e s ' s did

b) J a m e s :

Rate of return = i Z 6 J l 2000.00

Rate of return = 0 .438. ..

J a m e s ' s rate of return is 4 3 . 8 % .

J o h n n y ;

Rate of return = 2000 00

Rate of return = 0.447 Johnny ' s rate of return is 4 4 . 7 % . Johnny ' s rate of return is h igher than J a m e s ' s rate of re turn .

5. T h e pnnc ipa i is $900 ,


T h e c o m p o u n d i n g per iod is dai ly , or 365 t imes per year .

T h e te rm (in years ) is 1 year .


I used the f inanc ia l app l ica t ion on my calculator-Ky le 's annua l in terest rate w a s 10 .54%.

6- a) Ph i l : The principal is unknown. T h e annua l in terest rate is 6 .5%.

T h e c o m p o u n d i n g penod is sem i -annua l , or 2 t imes per year .


T h e fu tu re va lue is $125 000 .

Phi l inves ted a pnneipa l of $39 524 .63 .

L i n a : The principal is unknown.


T h e c o m p o u n d i n g penod is sem i -annua l , or 2 t imes per year



L ina inves ted a pnnc ipa i of 3 1 ' 4 ' - 7 .57 39 524.6 . > ' \:>f = 21 027 .06

Phi l inves ted $27 027 .06 more than Lina d id

b) T h e pnnc ipa i is $39 524 .63 .


T h e c o m p o u n d i n g per iod is sem i -annua l , or 2

t imes per year .



Lina w o u l d have $395 323 .07 in her accoun t af ter 36 years .

T a) Mel: The principal is unknown.




The fu ture va lue is $13 140.

Me l inves ted a pnnc ipa i of $7000 .02

M i k e : The pnncipai is unknown.


T h e c o m p o u n d i n g per iod is month ly , or 12 t imes per year.



Mike inves ted a pnnc ipa i of $5000 .12 .

Me l inves ted more pr inc ipal 10 years ago .


| j | f , a l ( . i i l , i l = - fl>«- H i v i - . t u . i ' u t V O I I H ; ; . t : V « y I w n v c : i r .

Mo! M i k o

^ P i i n c i p a l ( $ )

'\ I n t e r e s t R a t e p e r A n n u m

I C o i i i | J O u n d i n g p e r i o d

' V a l u e a t E n d o f Y e a r

/ o c i o o , ' hon i ) 1.-' i

o n i i u u l i i n o n t t i l y ]

; / o o o n?

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13

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1 0 ;( n

9 a n i ;

4

7 •11)') j

f 0 0 0 1

0 0 0 4

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T i m e

z m 6

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" 07414 O i Oct74 ' 4 | ^

: i ^ ; " " " f 1485 00 10744 4 4 _

i n " I " ^ ' 14140 00 {_ _ 1 3009 0 \

c) e .g. , T t i e f u t u r e v a l u e of y i k e ' s m v e s o m e n t w i l l

b e c o m e l a r g e r and g r o w f a s t e r t h a n t h e t u t u n . . v a l u e of

Mel 's i n v e s t m e n t . M i k e ' s i n v e s t m e n t e a r n s m o r e i n t e r e s t

a n d i s c o m p o u n d e d m o r e f r e q u e n t l y , s o t h e g r a p h is

s t e e p e r a n d m o r e c u r v e d .

8. B a n k A : T h e r e g u l a r p a y m e n t a m o u n t is $ 8 0 0 .

T h e p a y m e n t f r e q u e n c y is m o n t h l y , or 12 t i m e s per y e a r .


T h e p a y m e n t s a r e m a d e a t t h e end of e a c h p a y m e n t

p e r i o d .

T h e a n n u a l i n t e r e s t r a t e is 1 2 . 2 % . T h e c o m p o u n d i n g f r e q u e n c y is m o n t h l y , or 12 t i m e s per

y e s r .


B a n k A a c c o u n t i s w o r t h $84 3 1 9 . 8 1 .

B a n k B : T h e r e g u l a r p a y m e n t a m o u n t is $ 8 0 0 .

T h e p a y m e n t f r e q u e n c y i s m o n t h l y , or 12 t i m e s per y e a r .

T h e n u m b e r o f p a y m e n t s i s 72 .

T h e p a y m e n t s a r e m a d e a t t h e e n d o f e a c h p a y m e n t

p e r i o d .

T h e a n n u a l i n t e r e s t r a t e is 1 1 . 4 % .


t imes per year . The Mure value is unknown. Bank B accoun t is w o r t h $82 139 ,03 .

D i f fe rence : 84 319 .81 82 139 03 = 2180 .78

M a r y wi l l have $ 2 1 8 0 , 7 8 m o r e if she c h o o s e s

bank A,

i . a) J o s h : T h e regu lar p a y m e n t a m o u n t is $ 1 0 0 0 .

T h e p a y m e n t f r equency is annua l , or once per

year. T h e n u m b e r of p a y m e n t s is 4 5 .


p a y m e n t pe r iod . T h e annua l in terest rate is 634. T h e c o m p o o n d i n g f r equency is annua l , or o n c e per

ygar . The Mure value is unknown. Josh ' s i nves tmen t is wor th $212 7 4 3 . 5 1 . J e f f : T h e regu lar p a y m e n t a m o u n t is $ 3 0 0 0 . T h e p a y m e n t f r eguency is annua l , or o n c e per

yggf


T h e p a y m e n t s a re m a d e at the end of e a c h


T h e annua l in terest rate is 6 % . T h e c o m p o u n d i n g f r equency is a n n u a l , or o n c e per


J e f f s i nves tmen t is wo r th $ 6 9 827 .91

b ) J o s h : 1000(45) = 45 000

Jeff ; 3 0 0 0 ( 1 5 ) - 45 0 0 0

T h e y bo th inves ted $ 4 5 0 0 0 .

c ) Josh 3 1 . ' 7 4 3 . 5 1 •• 4 5 000 = 167 743 .51

Jeff ; 69 827 .91 - 4 5 0 0 0 = 24 827 ,91

Josh ea rned $167 743 .51 in interest and Jef f

ea rned $24 827 .91 in in terest .

d ) The regular payment amount is unknown.

T h e p a y m e n t f r equency is annua l , or once per

year. T h e n u m b e r of p a y m e n t s is 15. T h e p a y m e n t s a re m a d e at the end of each

p a y m e n t p e n o d . T h e annua l in terest rate is 6 % . T h e c o m p o u n d i n g f requency is annua l , or o n c e per

The ' f u tu re va lue is $212 7 4 3 , 5 1 ,

I used the f inanc ia l app l i ca t ion on my calcu lator ;

Jef f w o u l d need to depos i t $9140 ,05 every year for

15 yea rs to have the s a m e f inal va lue as J o s h .

10 . a) It is di f f icul t to pred ic t w h o wi l l be able to

pu rchase the more expens i ve car in f ive years

because the mon th l y depos i t a m o u n t s and

c o m p o u n d i n g rates a re ve ry s imi lar . D rew depos i t s

$200 per m o n t h tota l and has interest c o m p o u n d e d

b iweek ly . J o h n depos i t s a sl ight ly h igher month ly

amoun t , $ 2 1 7 . and his in terest is c o m p o u n d e d

sl ight ly less f requent ly (month ly ) .

1-26 C h a p t e r 1 ( I l a n c i a l M a t h e m a t i c s : I n v e s t i n g M o n e y

b | D r e w : T h e regular paymen t a m o u n t is $100 ,

T h e paymen t f r equency is b iweek ly , or 26 t imes per year .

T h e n u m b e r of paymen ts is 130,

T h e paymen ts are m a d e at the end of e a c h p a y m e n t p e n o d .

T h e annua l interest rate is 4 , 8 % ,

T h e c o m p o u n d i n g f requency is b iweek ly , or 26 t imes per year .


Drew wil i have $14 677 .43 in f ive yea rs .

John: T h e regular paymen t a m o u n t is $ 2 1 7 .

T h e paymen t f r equency is mon th ly , or 12 t imes per year T h e n u m b e r of p a y m e n t s is 60 .

T h e p a y m e n t s are m a d e at the end of e a c h p a y m e n t per iod .

T h e annua l interest rate is 4 . 8 % .

T h e c o m p o u n d i n g f requency is month ly , or 12 t imes per year


J o h n wil l have $14 682 .26 in f ive years ,

J o h n wii l be ab le to pu rchase a m o r e expens i ve car.

1 1 . a | i | R e g u l a r d e p o s i t i n v e s t m e n t : T h e regu lar p a y m e n t a m o u n t is $450 .

T h e paymen t f requency is quar ter iy . or 4 t imes per year T h e n u m b e r of paymen ts is 4 0 .

T h e paymen ts are m a d e at the end of each p a y m e n t

per iod .

T h e annua l in terest rate is 4 , 5 % .

T h e c o m p o u n d i n g f requency is quar ter ly , or 4 t imes per year. The future value is unknown.

T h e sav ings accoun t is wor th $ 2 2 575 ,07 ,

L u m p s u m i n v e s t m e n t : T h e pnnc ipa i is $ 5 0 0 0 ,

T h e annua l in terest rate is 6 % .

T h e c o m p o u n d i n g per iod is a n n u a l , or o n c e per year



T h e trust accoun t is wor th $ 8 9 5 4 . 2 4 .

To ta l : 22 575 .07 + 8954 .24 = 31 529 .31

T h e va lue of Chandra ' s port fo l io is $31 529 31

i i ) Pr inc ipa l : 450 (40 ) + 5000 = 2 3 000

Interest : 31 529 .31 ^ 23 000 = 8529 .31

Rate of return = ^ ^ 2 a 3 1

23 000

Rate of return = 0 .3708 . . .

Chand ra ' s rate of return is 3 7 . 1 % .

b ) No , she wil l not have e n o u g h for 4 yea rs

31 529 .31 - 10 000 = 21 529 .31

$21 529.31 inves ted for 1 year at 6 . 2 % c o m p o u n d e d annua l l y g rows to $22 864 .13 ,

22 8 6 4 , 1 3 - ^ 10 000 = 12 864 .13

$12 864 .13 inves ted for 1 year at 6 . 2 % c o m p o u n d e d annua l l y g rows to $13 6 6 1 . 7 1 ,

13 661 ,71 -- 10 000 = 3661 .71

$3661 .71 invested for 1 year at 6 . 2 % c o m p o u n d e d annua l l y g rows to $3888 .74 .

$ 3 8 8 8 . 7 4 is less than $10 000 , so C h a n d r a wi l l not have e n o u g h for 4 years .

^liMJ^MMol h.,tf,-. , .,r,-.:P . tMture va lue .

^ 2 r t f M ! O l _ _ _ ! P o r t f o l i o 2

-!OU Ch, _ _ r i„.>,ipr

j in!i->.,'.l '

I />.uiH,)i .!. i„r jP. ,.,

, 1>'3»)u

>, III ; , • . - , !

3 o n . ! uuii.;„l d e p o s i t s o f 31 .-oo ' -annya i

T h e C

C S B . P is $

4 = 4

I .<!• H.,y f .r-.,o<,i i i„ f . , io I f,..,r.}wrii.cfin

J .. '.h if,v.. . i l l , ' ) , h r i . s o f . i i / l l . , . Interest that is

• . , . . ip<.i i ' i4. .: nno 3<-t|M0 .t! / 1} -.r the ' ' ' 0 ' ' ' - 0 ' n4 por l io l iu 1 j .o 'o^.o.oi .c b) Port fol io 1: G I C : T h e pr inc ipa l is $25 000 . T h e annua l in terest rate is 8 .7%. T h e c o m p o u n d i n g per iod is annua l , or once per year .

T h e te rm (in years ) is 10 years ,

f o re value is unknown.

SIC is wo r th $57 575 .20 ,

n i . rt)

4 0 000 ; r i s 6 . 4 % or 0 ,064; f is 10

; 000 (1 + ( 0 , 0 6 4 ) ( 1 0 ) )

30

. is wor th $16 400

i n v e s t m e n t : T h e regu lar paymen t ^m . ' .s l ts $ 2 5 0 0 ,

T h e p a y m e n t f reguency is annua l , or once per year. T h e n u m b e r of paymen ts is 10.

T h e p a y m e n t s a re m a d e at the end of each p a y m e n t

per iod .


T h e c o m p o u n d i n g f requency is annua l , or once per year


T h e inves tmen t is wor th $31 298 35.

To ta l : 57 575 20 + 16 400 + 31 298 .35 = 105 2 7 3 55 Port fo l io 1 is wor th $105 273 .55 Portfol io 2:

G I C : T h e pnnc ipa i is $25 000 .


T h e c o m p o u n d i n g penod is month ly , or 12 t imes per year T h e te rm (in yea rs ) is 10 years .


T h e GIC is wo r th $59 485 .78 ,

C S B : T h e pnne ipa l is $10 000 .


T h e c o m p o u n d i n g per iod is annua l , or once per year T h e te rm (in yea rs ) is 10 years , Ttie future value is unknown

T h e C S B IS wo r th $18 595 86,

D e p o s i t i n v e s t m e n t : T h e regular paymen t a m o u n t is $ 1 2 5 0 0 ,

The p a y m e n t f r eguency is sem i -annua l , or 2 t imes per

year .

T h e n u m b e r of paymen ts is 20 ,

T h e p a y m e n t s a re m a d e at the end of each paymen t penod . T h e annua l in terest rate is 4 . 9 % ,

T h e c o m p o u n d i n g f requency is semi -annua l , or 2 t imes per year.


T h e inves tmen t is wor th $31 770 .60 .


Tota l 59 4 8 5 J 8 + 18 595 .86 + 31 770 ,60 = 109 852 24

Port fo l io 2 is wor t t i $ 1 0 9 852 .24 Port fo l io 2 is wor t t i m o r e t t ian por t fo l io 1 .

Chapter Task, page 7 3 A. Yes , t t iey can invest t he $ 6 0 0 0 n o w in a G I C tha t ea rns as h igh an mteres t rate as poss ib le and then beg in

invest ing thei r mon th l y sav ings in the sav ings accoun t ,

w h i c h ea rns a g o o d rate of in terest .

B . It wil l t ake abou t 32 yea rs . | | = 16 yea rs , so $ 6 0 0 0

4.5

wil l g row to 1 3 / .loQ in 16 yea rs a n d then $12 000 wi l l

g row to $24 000 in 32 years . )

T h e y a lso need to save m o n e y e a c h m o n t h to be ab le to

go in 3 years .

C S ince $23 T-'-.n 3 n 8 4 6 = $ 1 6 4 3 4 . they need a

regular p a y m e n t i nves tmen t w i th a fu tu re va lue of $16

4 3 4 , w h i c h wi l l requ i re a regu lar p a y m e n t of $431 .06 . There fo re , they need to save $431 .06 each m o n t h .

D. T h e y wi l l need to wa i t ano the r 4 m o n t h s . In 4 m o r e

mon ths , the i r sav ings a c c o u n t wi l l g r o w to $18 381 .33 a n d , c o m b i n e d w i th thei r G I C . w h i c h is stil l wo r th $ 6 8 4 6

(it wil l not ea rn any in terest ove r t hose 4 mon ths s ince

the c o m p o u n d i n g is annua l ) , t hey wi l l have $ 2 5 227 33,

T h e y wil l need $23 280 (1 ,08 ) = 25 142.40 .

C h a p t e r 1 D i a g n o s t i c T e s t , T R p a g e 5 6

— 1 2 I 4 S o / 3 9 1 0

A . (0, 100) . B . (3 , 200 ) . C . (6 . 300 ) . D. (9 , 4 0 0 )

b) Slope =

run

100 s lope = ^

c) b= 100

d) y mx t b

100

2 1 r. tiif.1 V pix • '.(I ti'-4 del.Minine s o m e po in ts

n l l h . ' U l O . U o u . . q . l t . 1 1 I } ( 1 ) + 50 = 60SO

•X n . ! f>'o -s .i [H.ml , 4. V lopo I no /o . ix. V) (2. 70) K 4, V 10.4) » no no, ( o y) (4 , 90 )

. h ./ 1(4Ol . SO 110 7) = (5 11 <' V 0 , lO i . q ' so 1 '0 (X V) ~- (8. 130) , 10 v 10(1(1. I 30 1.30. (/. ¥) = (10, 150)

V 10 A so

3{)()

4 so

4 0 0

yA)

T ) 0 h

« j O

1 3 0

SC

0

3

h t

. 5 4 4 / n ' 1(5

q -.li'.O,

654

gids

Ony<

3i.34

3«S<

X r 100

dec ima l - ^ = 1,110,., or 1.11 to two dec ima l p laces 589

percent : 1.11 • 100 = 1 1 1 %

4. a) $ 1 0 0 0 0 • 0.06 = $ 6 0 0 b) $25 000 - 0.06 =

$ 1 5 0 0 c) $50 0 0 0 • 0.06 = $ 3 0 0 0

5. a | $ 1 0 OOo 1 13 - 311 200

b ) $25 000 1 U S'41 000

c ) $50 000 I C- - $ 5 n 000

6. a ) | ; 0 . . 6 . , 4 . 0 . 4 2

0 I or A ; 1 , 5 d ) | ; 2 . 2 5

7. a) f h e pat tern is to add 71 to get the next

n u m b e r in the s e g u e n c e : 214 . 285 , 356 , 427, 498 ,

569

b) T h e pat tern is to add half of the n u m b e r to get

the next n u m b e r in the s e g u e n c e : 4 , 6. 9. 13.5,

20.25, 30 .375

c) T h e pat tern is the doub le the n u m b e r to get the

next n u m b e r in the s e q u e n c e ; 7, 14, 28 , 56 , 112,

224

3 y lOOx - 300

1-28 C h a p t e r ! t . oanc ia l M a t h e m a t i c s : i n v e s t i n g Money

can check the o ther n u m b e r x = ^^ Y= i

b | i) e .g. , S ince y = | + 1 is in the fo rm

y = + 6, I k n e w nght a w a y that the s lope of the

func t ion is ^ 2

c | V) e.g. , T h e def in i t ion of d o m a i n for a func t ion is the set of all poss ib le input va lues , i.e., x va lues . On a c o -ord ina te gr id , the x-axis is the def in i t ion of the d o m a i n d | II) e .g. . T h e def in i t ion of range for a func t ion is the set of al l ou tpu t va lues , s o m e t i m e s ca l led the c o - d o m a i n . O n a co-ord ina te g r id , the y -ax is is the range of the func t ion e | VI) e g. . T h e set o f in tegers is an e x a m p l e of d iscre te ' ma themat i cs , be ing a set of d ist inct , non -con t inuous ob jects .

f ) iii) e.g. . T h e set of real n u m b e r s is an e x a m p l e of con t inooos ma themat i cs , wh i ch have the proper ty o f

vary ing "smooth ly " or con t inuous ly .

g ) vi i) e .g. . T h e func t ion y = 3x + 7 is an e x a m p l e of a l inear re lat ion because it is in the l inear re lat ion f o rm y = mx + b.

, 0 25 1

3 . 0 ) . $ 1 1 0 0 1 , ^ 4 1-4 10

b) $ 8 9 - 0 .059 ^ t c 4 4

c ) $220 0 .0049 = $1 .08

4 . a , [ 2 , . O f ? ] 3 3 o , g 3 ^ ^

T o four dec ima l p laces , the a n s w e r is 8 .0169 .

. , ( 0 . 0 0 5 y m — 5 = 6 2 4 . 9 9 3 150

I. * 5 I

ir dec ima l p laces , the a n s w e r is 624 9932

0.001 348.. .

T o four dec ima l p laces , the a n s w e r is 0 .0013 .

, I 3.2 c ) —

• 12

5- a) (3 .46) (72 ,89) = 252 .1994

T o two dec ima l p laces , the a n s w e r is $252 20.

b) 7 . 6 9 ' = 4 5 4 , 7 5 6 . . .

T o two dec ima l p laces , the a n s w e r is $454 .76 ,

6. a | 7 y - 3 0 0 x * 5 6 0 0

- 3 0 0 x f 5600

-300 X ' 800

Th is egua t ion has a s lope of T ^

Slope = ^ run

s lope = T : 3 | 0

T h e nse is -300 and the run is 7, T h e y- in tercept is 800 ,

b) 7 y X 3500

7 y X 4 3500

S l o p e . ^ 5 ? run

y ^ 3.3500 slope ^

y = y + 5 0 0

T h e nse is 1 and the run is 7, T h e y- in tercept is 500 ,

7. a) per imeter : 2 • 6 + 2 • 2 = 16

per imeter 16 8 - 1 ^ ^ — or ^ ; 2 .67 ; 2 6 7 %


b) per imeter : 2 - 4 + 2 - U S = 1 6

P e f E ^ . l i ^ or ^ - 2 .875 ; 287 5 % length 4 8

c ) penmet . < • %2 = 12.4

P 2 * l t E = l M or ^ ; 2 .48 ; 2 4 8 % length 5 25

8. a) length

or 0 .375 per imeter ' 8

0 .375 • 100 = 3 7 . 5 %

b l J ? ^ ^ . = A or 0 .3478 . . . penmeter 23

0 .3478 . . . • 100 = 3 4 . 7 8 %

c l J £ ^ = 2 5 o r o . 4 0 3 2 . . .

perimeic- ,

0 .4032 . . . •^'^ 4 0 . 3 2 %

a A . 5 % • • 1 3 M ' O : $ 1 0 0 0 $50

B 6 % of I'4^1 $1050 • 0 . ' . 463

a 7 % o f 3 i ' 0 . % , . " 0 - 0 * ' i - . ' '

D. 2 . 4 % of $ 8 0 0 : $800 ^ 0 .024 = $19 .20

T h e order from g rea tes t to least is C. B, A , D.

10. a | :t . 'm.iio. ». i o ^ $ 4 1 7 5

$14:>0U • $ 3 I / S I f d o o r S

b) $51' .49 t) 13 - $9 OU

$59 5 $0 <-ij - 314', Ofl

C) 94 0 3 / 3 ».5

$ 1 5 0 . 9 8 + $22 .65 = $173 .63

1 1 . a) I; 0.33 b ) | ; 2 . 5 8

e l f ; 0 .87 C l f ; 1 0 . 2 5

12. a) T h e p a t t e m is to subt rac t 62 to get the nex t

n u m b e r in the s e q u e n c e : 587 . 525 . 4 6 3 . 4 0 1 , m 277

b) T h e pat tern is the add | of the n u m b e r to ge t the

next n u m b e r in the s e q u e n c e : 10. 12, 14,4. 17 ,28 ,

20 736 24 8832

i t h e pat tern is to doub le the n u m b e r to ge t t he nex t

n u m b e r in the s e g u e n c e : 3, 6, 12. 24 . 48 , 96

13. a) 3 - 4 x = 3 y - 2 x

= - 3 - ^ 2 x + 4 x

3 y 3 - 4 x ^ 2 x

3 y - -2x > 3

--2x i_3

3

y = X t 1 ^ 3

1 = 3;

y = ^^2 (3 ) + 1 ^ 3

y = ^ 2 + 1

y = .^1

b) x - 5 y + 8 - 3 *

^ 5 y - y = 3 * ^

' . y - 4

3 y = - x + 2

-^x + 2

X 2

, = 3: y = ^ ,

^ 3

1

y=^3

I 0.6 .

y = 1,023..

y 1.02

f 0.6 b) y = — + 7 ° ' ^ [ 52

y = 344.698. . .

y = 344.70

15. x = ^ 2 y + | z ; y = ^ | x + | z ; z = 3 x + 6 y

C h a p t e r 1 T e s t , T R p a g e 6 4

1 , a ) 2 0 ; Us ing the rule of 72 it wil l t ake 20 3.6

yea rs for her inves tment to doub le in va lue .

b) T h e pnnc ipa i is $ 3 6 0 0 .

T h e annua l in terest rate is 3 .6%. T h e c o m p o u n d i n g per iod is month ly , or 12 t imes

per year . The term (in years) is unt<nown. T h e fu ture va lue is doub le $ 3 6 0 0 , or $7200 .

I used the f inanc ia l app l ica t ion on my calculator :

T h e doub l ing t ime is 232 mon ths , or 19 years 4

m o n t h s

c ) Regu la r p a y m e n t inves tment : T h e regular

p a y m e n t amoun t is $15 , T h e p a y m e n t f reguency is month ly , or 12 t imes per

T t e n u m b e r of p a y m e n t s is 2 3 2 , the doub l ing t ime

for the f irst inves tment .




T h e c o m p o u n d i n g per iod is month ly .


1-30

C h a p t e r 1 . Pmancial M a t h e m a t i c s : Inves t ing Money

I used the f inanc ia l app l ica t ion on mv ca lcu la tor : T h e inves tmen t is wor th $7200.

T h e regular p a y m e n t i nves tmen t is wor th $5018.13. T h e s ing le p a y m e n t i nves tment has doub led to $ 7 2 0 0 . so it is wor th more

2. a) T h e p resen t va lue is $ 4 5 0 0 .


T h e c o m p o u n d i n g per iod is every two w e e k s , or 26 t imes

per year.


T h e fu ture va lue is $6000

I used the f inanc ia l app l ica t ion on my ca lcu la tor : He

w o u l d need 9 .607 . . . or 9 . 6 1 % annua l in terest

c o m p o u n d e d eve ry 2 w e e k s

b) i) The regular payment amount is unknown.

T h e paymen t f reguency is eve ry two w e e k s , or 26 t imes per year

T h e n u m b e r of paymen ts is 78 , 26 p a y m e n t s per year for 3 years .

T h e p a y m e n t s a re m a d e at the end o f e a c h p a y m e n t per iod

T h e annua l in terest rate is 9 . 6 1 % .

T h e c o m p o u n d i n g f r equency is every t w o w e e k s , or 26 t imes per year .

T h e fu ture va lue is $6000 ,

i used the f inanc ia l app l ica t ion on my ca lcu la tor : T revor ' s p a y m e n t s w o u l d need to be $ 6 6 . 5 1 ,

ii) 78 $66 51 =$5187 .84

$ 6 0 0 0 - $ 5 1 8 7 . 8 4 = $812.22 Trevor wou ld ea rn $812 .22 in interest .

V f / i' r r

A is $ 6 0 0 0 ; P is $3000 ; r i s 9 . 6 1 % or 0 0961

6000 = 3 0 0 0 + (3000) (0 .0961) ( f )

3000 = 288 .3 f

It w o u l d take 10.4 years , or 10 years 21 w e e k s for S3000 to g r o w to S6000

3. a) 30 years - 12 mon ths = 360 p a y m e n t s

360 • $ 2 5 0 = $90 000

b ) T h e regular paymen t a m o u n t is $250 .

T h e p a y m e n t f reguency is month ly , or 12 t imes per year T h e n u m b e r of paymen ts is 360 .


penod .


T h e c o m p o u n d i n g f reguency is month ly , or 12 t imes per year . T h e fu ture va lue is $155 000 .

I used the f inanc ia l app l ica t ion on my calcu lator ; T h e

a v e r a g e annua l interest rate w a s 3 .36%.

c ) The present value is unknown.


T h e c o m p o u n d i n g penod is month ly , or 12 t imes per year .



I used the f inanc ia l app l ica t ion on my ca lcu la tor ; Jess

w o u l d have had to depos i t $56 6 6 1 . 2 1 .

<';'•• -'A !. !• !o v - . l i n . .-.'6 the g rea te r ' • 3 (•'. f -f.-'ii Of. tic ' h-)V. : i , , - . ' !•(>!,nts have the ' i'.i-- 'uii- . , s . i , ' 4: f ,t,. ,|,. , : . , , , , ,ent

• H " " U ! • . . t ' l i ^ o ,, h • . . Mount to be

4 <<| 4.1C I I r [... •.( ,. ^ I „ ; , o , - ' 0 0 { .

: n. , <i,. i,«l ,tii. r^ ... I ; j

I Ot, -O .1, <4 MO p.-ir i ,',

t ' o - ' I'U O j< <, ] ' . ] • '

111< hilt HI ^. •III" I mik.'o-i:.

' ' ' • >•*• •«of'i' ' *••• o ; < a lcy la tor : f •'••••^ < :' iP-'4t J ' .,' . s . ' . i 0 5 J 3 8 . . ,

Rosnvrs tc fl C i C M.^^ ,. ... : , . , , „ , , ' 4 0 0 .38

13' - n n u a l interest rate is 4 .5%.

pound ing per iod is annua l .

13. I M ( in years ) is 10.

'"' "e value is unknown.

e f inanc ia l app l ica t ion on my ca lcu la tor :

.™.-e va lue of the second G IC is $ 4 8 2 3 . 4 2 8 ,.

R E S P : T h e regu lar p a y m e n t a m o u n t is $25 .

T h e p a y m e n t f r equency is month ly , or 12 t imes per year.

T h e n u m b e r of paymen ts is 240 . 12 t imes per year for 20 years .

T h e p a y m e n t s a re m a d e at the end of each p a y m e n t p e n o d .


The c o m p o u n d i n g f reguency is month ly , or 12

t imes per year.


I used the f inanc ia l app l ica t ion on my ca lcu la tor

T h e fu ture va lue of the R E S P is $8966 132 ,

T F S A : T h e regular p a y m e n t a m o u n t is $50 ,

T h e p a y m e n t f r eguency is month ly , or 12 t imes per year.

The n u m b e r o f p a y m e n t s is 48 . 12 t imes per year for 4 years .

T h e p a y m e n t s are m a d e at the end of each paymen t p e n o d .



t imes per year .


I used the f inanc ia l app l ica t ion on my calcu lator :

The future va lue of the T F S A is $ 2 5 2 1 . 3 4 3 . ..

Tota l va lue of i nves tment port fo l io on L e n s 20 th bir thday:

$4823 .428 . . . + $ 8 9 6 6 . 1 3 2 . . + $2521 343 = $16 310 90

b) A m o u n t inves ted : G IC ; $2000 ;

R E S P ; $25 • 240 = $ 6 0 0 0 ; T F S A : $50 • 48 = $ 2 4 0 0

$ 2 0 0 0 + $ 6 0 0 0 + 2 4 0 0 = $10 4 0 0

$10 400 w a s inves ted a l together .

F o u n d a t i o n s of Ma themat ics 12 S o l u t i o n s Manua l 1-31

5 a) t ' . r i - i ' ' . j Hir 11)'In.

GIC. I |M<>%s;iil v . j l u t ; i s 'T.'iOOO

111..- a i i i . u . i l i n l f U ' s f i-iU* i:i 'J /"•..

I h . . ( uiii|.nuitdinf) |.i.'ii«)d IS .itinuul

1 h i ; h-Ain (tn v < M i f . } r- 4

/ / i f / u l J i / i - i / .4jH' iiiihinw^u

\ i,:....f| l i n - i i n a i K . i a l j | .p l i ( . a t i f>n (>n i n y < a lcu lator ; T h e

f i iU in ' v a l i H - t»l t l u - ( 4 C i;, %:\A?,f . 3 4 ) .

C S B : I h c f . H s e n t v a k » : 1 : ; $ 1 hlHJ

rti(> a n n u . i l i t i t f r < ; s l r a l e : i s n.n':/.,

1 h.> ' • . inipoetMiiiKj pr ' i iot l I S - i n i m , ) !

I ht. tc'fir; n n v - m h 1- 3

i . ' i" 44 i i / f ; t ' . - 4 i ;< - - i i n k m m n

I a s f n l 11,1; i i n a i K . i H i u p p i i f a l i f i i 'S i i s i y sa lcu la tor : T h e

l u h i i . ' vAhv l i n ; ( ' .:>[{ is . $ 1 0 4 1 n 4 . i

S a v i n g s a t ^ e o o n t : ! I K ; n : g u l ; i i e - j y n u m t a m o u n t is $25 .

ffif: p . i y u H ' i i ' h ' ;gu«;nr ,y r , v^«:<43-/ <<'. '^i t imes per year .

, 0 , , , , , i u .r - i iMoi ' ts ... : ' 4 n t imes per year for

ments are m a d e at the e n d of e a c h p a y m e n t

ual in terest rate is 2 . 5 % , . - r f ipoynding f r equency is week l y , or 52 t imes per

4n. ; uo

)!

• rp .1 •

,/• I M 4

' 1 4

Th

year.

r e value is unknown.

. . . ^ , the f inanc ia l app l ica t ion on my ca lcu la tor i -«^

fu tu re va lue of the sav ings accoon t is $ 6 9 2 1 . 9 4 9 . . .

Cur ren t va lue ;

$ 3 3 3 7 , 3 5 9 . . . + $ 1 6 9 1 . 5 4 3 . . . + $ 6 9 2 1 . 9 4 9 . . .

= $11 950 85

Lou 's por t fo l io ;

B o n d : A = P(1 + rt)

P i s $ 1 0 0 0 ; r i s 2 . 8 %

A = 1000(1 + 0 . 0 2 h p i j ) 1,1114

C S B : T h e presen t valuu- $ 1 3 6 0 .

T h e annua l in terest o n o / < 3 ' , , T h e c o m p o u n d i n g per iod is s e m i - a n n y a l .


Tf ie fof t i re va lue is onl r r iowf i .

I used the f inanc ia l app l ica t ion on my ca lcu la tor : T h e

fu tu re va lue of t he C S B is $ 1 1 7 8 . 0 6 8 . . .

S a v i n g s a c c o y n t : T h e regu lar p a y m e n t a m o u n t is $125 ,

T h e p a y m e n t f r equency is mon th l y , o r 12 t imes per year .

T h e n u m b e r of p a y m e n t s is 7 2 , 12 t imes per year for 6

years .

T h e p a y m e n t s a re m a d e at the end of e a c h p a y m e n t

per iod . T h e annua l in terest rate is 2 . 1 5 % . T h e c o m p o u n d i n g f r eguency is month ly , or 12 t imes per

y03r The future value is unknown.

I used the f inanc ia l app l i ca t ion on my calcu lator ; T h e

fu ture va lue of the sav ings accoun t is $ 9 5 9 7 . 1 2 6 . . .

Cur ren t va lue ; $ 1 1 1 2 + $ 1 1 7 8 . 0 6 8 . . . + $9597 126 . . . = $11 887 .19

b) G reg ' s por t fo l io ;

A m o u n t i nves ted : G I C ; $ 3 0 0 0 ; C S B ; $ 1 5 0 0 ,

Sav ings ; $ 2 5 • 260 = $ 6 5 0 0

$ 3 0 0 0 + $ 1 5 0 0 + 6 5 0 0 $ 11 uOO

Interest e a r n e d ; $11 950 .85 - $11 000 = $950 85

950.85 Rate of return = ^

Rate of re tum = 0 086. . . or 8 .6%

O i o o o n I .!.•/( sf( d h f .nd $ 4 M M : i j , e $ 1 0 0 0 ;

L . V i . s q s 3 1 2 5 ,% $ 5 9 ( 4 )

rU)("> ^ ' I C O ' M I » 'i[)()()<) %1 0ni3

|.4--f</.f . "un i . :d :i 1 1 0 8 / / u . ' 4 ' 0 = $887 .20

887.20 Rate of return = ^

Rate of return = 0.080.. or 8 . 1 %

Greg has a sl ight ly g rea te r rate of re turn.

1-32 Chaptof I Ir m a n c i a i M a t h e m a t i c s : Invest ing Money

investing money solutions

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