1 using the financial calculator copyright by diane scott docking 2015

1

Using the Financial Calculator

Copyright by Diane Scott Docking 2015

Learning Objectives

To learn how to use the Financial Calculator

Copyright by Diane Scott Docking 2015 2

3

TI BA II+ Calculator Setup—Follow This!!

Use one period per year: P/Y = 1

[P/Y] 1

Set decimal to 6 places: Format DEC=6

[FORMAT] 6

Set BGN register to “END”


2ND ENTER

2ND ENTER

4

Financial Calculators—TI BA II+

N

I/Y

PMT

FV

PV

Number of time periods

Interest rate (%)

Future Value

Present Value

Payment

Basic Calculator Keys


5

Financial Calculators—TI BA II+

Has embedded formulas

Five time value keys: N, I/Y, PV, PMT, FV• Use either four or five keys

• Interest rate (I/Y) is entered as a whole number, not a decimal (e.g. 7% is entered as 7)

• PV and FV must carry opposite signs (‘+’ or ‘-’)• PMT must carry the same sign as either the PV or the FV,

whichever is appropriate

Some calculators distinguish between inflows and outflows

Cash flow sign convention: If a PV is entered as negative the computed FV is positive


6

Time is Money

$100 in your hand today is worth more or less than $100 in one year?Money earns interest

• The higher the interest rate, the faster your money grows

Q: How much would $1,000 promised in one year be worth today if you could be earning 12% interest?


7

Time is Money

A: $1,000/(1.12)1 = $892.86


t0 t1

$1,000PV

So

Verify: $892.86 x .12 = $ 107.14 interest earned plus initial investment = $ 892.86

yields = $1,000.00

Financial Calculators & Cash Flow Sign Convention

Input $1,000 FV Input 12 I/Y Input 1 N Input 0 PMT Calculate PV (Cpt PV)

Is PV positive or negative? Why? What’s the deal?

Here are the key strokes:

1000 12 1 0

PV will be NEGATIVE. A -$892.86. But answer is $892.82.

By convention we put PV in as a negative number, so that FV will be positive.

Ignore the negative sign. The negative sign simply means you invested (had a cash outflow).


FV

I/Y

N

PMT

CPT PV

9

1. FV of a Lump Sum: What’s the FV of an initial $100 investment after 3 years if i = 10%?

FV = ?

0 1 2 310%

100


$100 x .10 = Interest $ 10 Principal $100 Balance $110 x .10 = interest $11

balance $110 Balance $121 x .10 = interest $ 12.10

balance $121.00 FV = $133.10

$100 x .10 = $10 x 3 yrs. = $30 in interest if withdraw interest each year.

Financial Calculator Input: FV of a Lump Sum

Input -$100 PV Input 10 I/Y Input 3 N Input 0 PMT Calculate FV (Cpt FV)

Is FV positive or negative? Why? What’s the deal?


100 10 3 0

FV will be a POSITIVE $133.10.



PV

I/Y

N

PMT

CPT FV

+│─

11

Another Example: FV of a Lump Sum

Mary invests $1,000 today for 20 years @ 8%. How much will she have in 20 years?

FVn = PV(1+i) n FV20 = $1,000 (1.08)20 = $4,660.96


Here are the key strokes: 1000 8 20 0

FV will be a POSITIVE $4,660.96


Input -$1000 PV Input 8 I/Y Input 20 N Input 0 PMT Calculate FV (Cpt FV)

+│─ PV

I/Y

N

PMT

CPT FV

12

2. PV of a Lump Sum: What’s the PV if i = 10% to end up with FV = $100 after 3 years?

FV = 100

0 1 2 310%

75.13


Verify:$75.13 x .10 = Interest $ 7.51

Principal $75.13 Balance $82.64 x .10 = interest $ 8.26

balance $82.64 Balance $90.90 x .10 = interest $ 9.09

balance $90.90 FV = $99.99 = $100

$100 /(1.10)3 = $75.13

Financial Calculator Input: PV of a Lump Sum

Input $100 FV Input 10 I/Y Input 3 N Input 0 PMT Calculate PV (Cpt PV)


100 10 3 0

PV will be a NEGATIVE $75.13.

Ignore negative sign. Answer is $75.13.


FV

I/Y

N

PMT

CPT PV

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3. FV of an annuityExample 1: What is the FV of a 3-year

ordinary annuity of $100 at 10%?

$100 100100

0 1 2 310%

FV =

10% 10%


110121

100(1.10)=

100(1.10)2=

$331

Input $0 PV Input 10 I/Y Input 3 N Input $100 PMT Calculate FV (Cpt FV)


0 10 3 100

FV will be a NEGATIVE $331. Ignore negative sign. Answer: $331.

Cannot put 0 in as a negative.


PV

I/Y

N

PMT

CPT FV

Financial Calculator Input: FV of an ordinary annuity

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Example 2: What’s the FV of a 3-year annuity due of $100 at 10%?

100$100 100

0 1 2 310%

FV = Copyright by Diane Scott Docking 2015

100(1.10)= 110100(1.10)2= 121

133.10100(1.10)3=

$364.10

Set calculator to BGN mode

Input $0 PV Input 10 I/Y Input 3 N Input $100 PMT Calculate FV (Cpt FV)


[BGN] [SET]

0 10 3 100

FV will be a NEGATIVE $364.10. Ignore negative sign. Answer: $364.10.



PV

I/Y

N

PMT

CPT FV

Financial Calculator Input: FV of an annuity due

2ND 2ND

18

4. PV of an annuityExample 1: What’s the PV of an 3-year

ordinary annuity of $100 per year at 10%?

100 100100

0 1 2 310%

= PVCopyright by Diane Scott Docking 2015

=100/(1.10)1

90.91=100/(1.10)2

82.64

75.13

$248.68

=100/(1.10)3

Reset calculator to END mode

Input $0 FV Input 10 I/Y Input 3 N Input $100 PMT Calculate PV (Cpt PV)


[BGN] [SET]

0 10 3 100

PV will be a NEGATIVE $248.68. Ignore negative sign. Answer: $248.68.



FV

I/Y

N

PMT

CPT PV

2ND 2ND

Financial Calculator Input: PV of an ordinary annuity

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Example 2: What’s the PV of an 3-year annuity due of $100 per year at 10%?

100 100

0 1 2 3

10%

100

= PV


90.91=100/(1.10)

82.64=100/(1.10)2

273.55

Reset calculator back to BGN mode

Input $0 FV Input 10 I/Y Input 3 N Input $100 PMT Calculate PV (Cpt PV)


[BGN] [SET]

0 10 3 100

PV will be a NEGATIVE $273.55 Ignore negative sign. Answer: $273.55



FV

I/Y

N

PMT

CPT PV

2ND 2ND

Financial Calculator Input: PV of an annuity due

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Example: What is the FV of this uneven cash flow stream if rates are 10% and payment is made at end of the year?

0

100

1

300

2

300

310%

-50

4


300 x (1.10) =

300 x (1.10)2 =

100 x (1.10)3=

330363133.10

FV = $776.10

Using Calculator for Uneven CFs


Input $0 CF0

Input $100 CF1

Input $300 CF2

Input $300 CF3

Input -$50 CF4

Input 10% interest Calculate FV

Here are the key strokes: [BGN] [SET]

0 , C01 appears,

100 ,F01 appears,1 ,C02 appears



50 ,F04 appears, 1 , C05 appears

, I= appears, 10 , NPV= appears,

NPV = 530.09 appears. This is the PV of the CFs.

Continued>>>>>>>>>>>


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CF

CPT

NPV

2ND

ENTER ↓

2ND

ENTER ↓ ENTER ↓

ENTER ↓ ENTER ↓

+│─ ↓

ENTER ↓

ENTER ↓

ENTER ↓

↓ENTERENTER

Financial Calculator Input:FV of uneven cash flows

Input $530.09 PV Input 10 I/Y Input 4 N Input $0 PMT Calculate FV (Cpt FV)


530.09 10 4 0

FV will be a $776.10.


PV

I/Y

N

PMT

CPT FV

Financial Calculator Input:FV of uneven cash flows (continued)

+│─

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Example: What is the PV of this uneven cash flow stream if rates are 10% and payment is made at the end of the year?

0

100

1

300

2

300

310%

-50

4

90.91

______

$530.08 = PVCopyright by Diane Scott Docking 2015

=100/(1.10)

=300/(1.10)2

=300/(1.10)3

=-50/(1.10)4

247.93

225.39

-34.15


Input $0 CF0

Input $100 CF1

Input $300 CF2

Input $300 CF3

Input -$50 CF4

Input 10% interest Calculate PV

Here are the key strokes: [BGN] [SET]

0 , C01 appears,




50 ,F04 appears, 1 , C05 appears

, I= appears, 10 , NPV= appears,

NPV = 530.09 appears. This is the PV of the CFs.


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CF

CPT

NPV

2ND

Financial Calculator Input:PV of uneven cash flows

ENTER ↓

2ND

ENTER ↓ ENTER ↓

ENTER ↓ ENTER ↓

+│─ ↓

ENTER ↓

ENTER ↓

ENTER ↓

↓ENTERENTER

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Agree to make “step payments” on a contract as follows:

$1,000 per month for the first year

$1,300 per month for the second year

$2,000 per month for the third year

At 10% annual rate, what is the PV of these payments?

Example: PV of Monthly Uneven Cash Flow Stream


Make sure calculator is set to END mode

Input $0 CF0

Input $1000 CF1-12

Input $1300 CF13-24

Input $2000 CF25-36

Input 10%/12 =0.83333% interest

Calculate PV

Here are the key strokes: [CLR WORK] 0 , C01 appears,

1000 ,F01 appears, 12 ,C02 appears



, I= appears, 10 12 , I=0.833333 appears

, NPV= appears,

NPV = 43,400.52 appears. This is the PV of the CFs.


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CF

CPT

NPV

ENTER ↓

ENTER ↓ ENTER ↓

ENTER ↓ ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

Financial Calculator Input: PV of Monthly Uneven Cash Flow Stream

=

2ND CF 2ND

÷

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Recall the formula:

We can use the Financial Calculator to solve for EAR.

Calculating Effective Annual Rates with a Calculator


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m

Nom

m

iEAR

Where: m is number of compounding periods per year.

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Example: EAR% for a nominal rate of 8%, compounded quarterly? Daily?


TO PRESS DisplaySelect Interest Conversion [ICONV] NOM = 0

Enter nominal interest rate 8 NOM = 8.00

Enter # of compounding periods per year

4 C/Y = 4.00

Compute EAR EFF = 8.243%


365 C/Y = 365.00


2ND

ENTER

↓ ↓ ENTER

CPT↑

↑ ↑

↑ CPT

ENTER

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Example: EAR% for a nominal rate of 10%, compounded semi-annually, quarterly, monthly, and daily?


TO PRESS DisplaySelect Interest Conversion [ICONV] NOM = 0

Enter nominal interest rate 10 NOM = 10.00


2 C/Y = 2.00



4 C/Y = 4.00



12 C/Y = 12.00



365 C/Y = 365.00


2ND

ENTER

↓ ↓ ENTER

CPT↑

↑ ↑

↑ CPT

↑ ↑

↑

↑ ↑

↑

CPT

CPT

ENTER

ENTER

ENTER

Finding “n” and “i” of a Lump Sum

It is EASY to find “n” and “i” using a Financial Calculator

FV & PV of a lump sum: Example 1: At what interest rate would you have to

invest $100 today to end up with $133.10 in 3 years?


Input - $100 PV Input $133.10 FV Input 3 N Input $0 PMT Calculate I/Y (Cpt I/Y)


100 133.10 3 0

I/Y = 10%

FV

I/Y

N

PMT

CPT

PV+│─

Finding “n” and “i” of a Lump Sum

FV & PV of a lump sum: Example 2: If you invest $100 today at 10%, how long

will it take to grow to $133.10?


Input - $100 PV Input $133.10 FV Input 10 1/Y Input $0 PMT Calculate N (Cpt N)


100 133.10 10 0

N = 3 years

FV

N

I/Y

PMT

CPT

PV+│─

Finding “n”, “i”, and “payment” of Annuities

It is EASY to find “n”, “i”, and “payments” using a financial calculator.

FV & PV of an ordinary annuity: Example 1: At what interest rate would you have to

invest $100 payments made annually (at end of year) to end up with $331 in 3 years?

Example 2: If you invest $100 annually (at end of year) at 10%, for how many years must you invest before your future value equals $331?

Example 3: How much must you invest annually (at end of year) at 10%, for 3 years to accumulate a future value of $331 at the end of 3 years?



Finding “i”

FV & PV of an ordinary annuity: Example 1: At what interest rate would you have to

invest $100 payments made annually (at end of year) to end up with $331 in 3 years?


Input $0 PV Input - $331 FV Input 3 N Input $100 PMT Calculate I/Y (Cpt I/Y) Need to make FV or payments negative.


0 331 3 100

I/Y = 10%

FV

I/Y

N

PMT

CPT

PV

+│─


Finding “n”

FV & PV of an ordinary annuity: Example 2: If you invest $100 annually (at end of year)

at 10%, for how many years must you invest before your future value equals $331?


Input $0 PV Input $331 FV Input 10 1/Y Input -$100 PMT Calculate N (Cpt N)


0 331 10 100

N = 3 years

FV

N

I/Y

PMT

CPT

PV

+│─


Finding “payment”

FV & PV of an ordinary annuity: Example 3: How much must you invest annually (at end

of year) at 10%, for 3 years to accumulate a future value of $331 at the end of 3 years?


Input $0 PV Input $331 FV Input 10 1/Y Input 3 N Calculate Pmt (Cpt Pmt)


0 331 10 3

Pmt = -$100

FV

N

I/Y

PMTCPT

PV


It is EASY to find “n”, “i”, and “payments” using a financial calculator.

FV & PV of an annuity due: Example 1: At what interest rate would you have to

invest $100 payments made annually (at beginning of year) to end up with $364.10 in 3 years?

Example 2: If you invest $100 annually (at beginning of year) at 10%, for how many years must you invest before your future value equals $364.10?

Example 3: How much must you invest annually (at beginning of year) at 10%, for 3 years to accumulate a future value of $364.10 at the end of 3 years?



Finding “i”

FV & PV of an annuity due: Example 1: At what interest rate would you have to

invest $100 payments made annually (at beginning of year) to end up with $364.10 in 3 years?



Input $0 PV Input -$364.10 FV Input 3 N Input $100 PMT Calculate I/Y (Cpt I/Y)


[BGN] [SET]

0 364.10 3 100 I/Y = 10%

PV

I/Y

N

PMT

CPT

FV

2ND 2ND

+│─


Finding “n”

FV & PV of an annuity due: Example 2: If you invest $100 annually (at beginning of

year) at 10%, for how many years must you invest before your future value equals $364.10?



Input $0 PV Input -$364.10 FV Input 10 I/Y Input $100 PMT Calculate N (Cpt N)

Here are the key strokes: Already at BGN

0 364.10 10 100 N = 3

PV

I/Y

N

PMT

CPT

FV+│─


Finding “payment”

FV & PV of an annuity due: Example 3: How much must you invest annually (at

beginning of year) at 10%, for 3 years to accumulate a future value of $364.10 at the end of 3 years?



Input $0 PV Input -$364.10 FV Input 10 I/Y Input 3 N Calculate Pmt (Cpt Pmt)

Here are the key strokes: Already at BGN

0 364.10 10 3 PMT = $100

PV

I/Y

N

PMTCPT

FV+│─

42

Constructing Amortization Schedules using the Financial Calculator

Construct an amortization schedulefor a $1,000, 10% annual rate loanwith 3 equal payments in arrears (paid at end of year).


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Step 1: Find the required payments.

PMT PMTPMT

0 1 2 310%

-1,000

3 10 -1000 0

INPUTS

OUTPUT

N I/Y PV FVPMT

402.11

Amortization Schedule Using Calculator


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2nd AMORT:

Amortization Schedule using Calculator


P1 = ___ P2 = ___

BAL = _______ PRN =______ INT =______

P1 = ___ P2 = ___

BAL = _______ PRN =______ INT =______

P1 = ___ P2 = ___

BAL = _______ PRN =______ INT =______

-697.89 302.11 100.00

enter

enter 1 1

2

Ignore negative sign

2

3 3

enter

enter

enter

enter

-365.56 332.33 69.79

365.56 0 36.56

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BEG PRN ENDYR BAL PMT INT PMT BAL

1 $1,000 $402.11 $100 $302.11$697.89

2 697.89 402.11 69.79 332.33 365.56

3 365.56 402.12 36.56 365.56 0

TOT 1,206.34 206.35 1,000


Amortization Schedule using Calculator

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Example: Amortization of a Real-World Mortgage (and why to stay home with mom and dad)

Buy a $300,000 house with 20% down Finance $240,000 at 6% over 30 years Questions:

What are your monthly mortgage payments?For the first year, how much did you pay in interest and

principal?What is the loan balance at the end of year 5?For the 12th monthly payment, how much did you pay in

interest and principal?How much total interest did you pay in years 1 through 5?


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Example: Amortization of a Real-World Mortgage

Questions:What are your monthly mortgage payments?


N = 30 yrs x 12 = 360 paymentsI/Y = 6%/12 = 0.50%

INPUTS

OUTPUT 1,438.92

360 .50 -240,000 0

N PMTI/Y PV FV

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Questions:For the first year, how much did you pay in interest and

principal? Keep payment information in calculator.

2nd AMORT:


P1 = ___ P2 = ___

BAL = ___________

PRN =___________

INT =____________

-237,052.77

2,947.23

14,319.83

enter

enter 1 12



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Questions:What is the loan balance at the end of year 5?

Keeping everything the same in the calculator

Bring back up to P1 by hitting the ↑ two times.


P1 = ___ P2 = ___

BAL = ___________ -223,330.46

enter

enter 60 60



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Questions:For the 12th monthly payment, how much did you pay in interest

and principal? Keeping everything the same in the calculator

Bring back up to P1 by hitting the ↑ four times.:


P1 = ___ P2 = ___

BAL = ___________

PRN =___________

INT =____________

-237,052.77

252.40

1,186.53

enter

enter 12 12



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Questions:How much total interest did you pay in years 1 through 5?

Keeping everything the same in the calculator

Bring back up to P1 by hitting the ↑ four times.:


P1 = ___ P2 = ___

BAL = ___________

PRN =___________

INT = ____________

-223,330.46

16,669.54

enter

enter 1 60



69,665.73

1 using the financial calculator copyright by diane scott docking 2015

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