Problem Data

I = 0.02

n = 6

PMT = 200

Solution

(1+i)^(n) = 1.126162

(B9-1)/I = 6.308121

B10*(1+i) = 6.434283

FV = 1286.857

Future Value of Payment

Future Value of an Ordinary Annuity

Problem Data

I = 0.05

n = 10

PMT = 13000

Solution FV 163512.60

(1+i)^(n) = 1.628895Sum of

Payments 130000

(B9-1)/(i) = 12.57789 Interest 33512.60296

FV = 163512.60

Reinvestment Interest

Note that cents are the first two decimal places

Problem Data

PV = 200 10939.56

n = 4 9261.00

I = 0.03 16537.50

21000.00

Solution 57738.06

FV = PV*(1+i)^n

FV = 225.10

Future Value of a Deposit

Annuity Due

Problem Data

I = 0.08

n = 13

PMT = 3000

Solution

(1+i)^n = 2.719624

(B9-1)/I = 21.4953

(B10)*(1+i) = 23.21492

FV = 69644.76

FV -> Nominal Interest Rate

Problem Data

PV = 4094

FV =

n (Deposit Period in Yrs) = 0.082191781

I (Nominal Interest Rate) = 0.186

m (Compounding Periods) = 365

i/m = 0.000509589

n*m = 30

Solution

FV = PV*(1+i/m)^(n*m)

FV = 4157.052396

Problem Data

PV = 2096

FV = 4682

n = 9

I =

Solution

I = (FV/PV)^(1/n)-1

I = 9.34%

Interest Rate of an Investment

Problem Data

PV = 300

FV = 25000

n =

I = 0.08

Solution

n = log(FV/PV)/log(1+i)

n = 57.46866939

Number of Periods of an Investment

In the final computing interval, what is the dollar amount of interest that is earned from earlier interest (rather than off of the original principal)?

330.75

Problem Data 315

PV = 300 15.75

FV = 15

n = 1 0.75

I = 0.1

m = 2

i/m = 0.05

n*m -1 = 2

Solution

FV = PV*(1+i/m)^(n*m-1)

FV = 330.75

Subtract e4 - e5

FV(n*m-1)

Time Deposit

FV(n*m)

Subtract e2 -e3

PV(i/m)

In the final computing interval, what is the dollar amount of interest that is earned from earlier interest (rather than off of the original principal)?

Effective Interest Rate

Problem Data

I = 0.05

m = 2 0.050625

i/m = 0.025

0.050625

I = (1+ i/m)^m-1

I = 0.050625

Problem Data

FV = 3700

PV =

n = 23

I = 0.11

Solution

PV = FV*(1+i)^(-n)

PV = 335.5623383

Value place of Each Opportunity

PV of Nominal Interest Rate

Problem Data

FV 90000

PV

n 8

i 0.09

m 2

i/m 0.045

n*m 16

Solution

PV FV*1(1+i/m)^(n*m)

PV 44502.24

PV of Discount Rate

Problem Data

FV 2700

PV

n 20

i 0.12

Solution

PV FV*(1+i)^(-n)

PV 279.90

PV of Mixed Cash Flows

Problem Data

FV 4000 5555.556

PV 2572.016

n 3 3175.329

i 0.08

Solution

PV FV*(1+i)^(-n)

PV 3175.329

PV Annuity PV Perpetuity

Problem Data Problem Data

I 0.09 PMT 20000

n 4 I 0.05

PMT 1000

Solution Solution

1/(1+i)^(n) 0.708425 PMT/i 400,000.00

PVIFA 3.23972

PV 3239.72

63239.72

3239.72

Retirement Annuity Due

Problem Data

i 0.038

m 26

i/m 0.0014615

n 27

n*m 702

PMT 4615.38

Solution

1/(1+i/m)^(n*m) 0.3587064

PVIFA 438.77981

PVIFA*(1+i/m) 439.4211

PV 2028095.37

PV of Stream of Cash Flows PV of first year

PV of 2nd Year

Problem Data PV Ordinary Annuity of remaining years

FV 24000 Annuity PV 23105.360

PV Add with other cashflows 19645.963

n 2 128783.2

i 0.087 171534.5

Solution

PV FV*(1+i)^(-n)

PV 20311.98

23919.04

20311.98

117956.17

162187.19

152166.2

PV annuity Due PV of single Cash Flow

i 0.087 FV 139373.35

n 17 PV

pmt 16000 n 2

i 0.087

Solution

1/(1+i)^(n) 0.24216

PVIFA 8.710834 Solution

PV 139373.35 PV

PV 117956.17

Go Backwards

Problem Data

PV = 10000

n = 40 19668.99

I = 0.04 11916.8

7280

Solution 38865.79

FV = PV*(1+i)^n

FV = 48010.21

Mixed Stream of Cash Flows

Calculation PMT

Problem Data

i 0.08

n 40

FV 48010.21

Solution

(1+i)^(n) 21.72452

FVIFA 259.0565

PMT 185.3272

problem data

i 0.08

m 12

i/m 0.006667

FV 25000

PMT 300

Solution

0.441833

0.006645

n 5.541299

Problem Data 722572.47

i 0.06 651944.00

m 12 70628.47

i/m 0.005

n 4

n*m 48

PMT 150

Solution

0.787098

42.58032

6387.05

How many months will it take for you to pay off the balance of late paying a bill

Problem Data

i 0.008

PV 16360.55

PMT 340

Solution

ln -0.48606

ln (1+i) 0.007968

n -61.00

Payment of an

Ordinary Annuity

(Amortization)

Problem Data

i 0.10 Principal 346441.17

n 25

Interest

Owing at

end of

year 34644.12

Principal 350,000

Solution

1/(1+i)^n 0

PVIFA 9.07704002

PMT $38,558.83

Interest Owing at the end of year = Principal oustanding X

Interest Rate

Problem Data

Principle

Owing $342,526.46

Interest Owing at the end of year = Principal oustanding X

Interest RatePrincipal Owing = Principal Outstanding - (Loan

Payment - Interest Owing)

Problem Data

Present Value of an

Ordinary AnnuityPrincipal

Borrowed 200000

Problem Data PV 190909.5

i 0.08 Repaid 9090.54

m 1

i/m 0.08

n = Total - year pass 18

n*m 18

PMT 20370.44

Solution

1/(1+i/m)^(n*m) 0.250249

PVIFA 9.371887

PV 190909.5

Interest in

Payment

# of Payments 36

Payments 3087.71

Principal 100000

Interest 11157.56

Total amount of

interest paid over life

of loan

Buy a Car & Borrow,

what are monthly

payments

Problem Data

i 0.073

m 12

i/m 0.006083

n 5

n*m 60

Principal 94000

Solution

1/(1+i/m)^(n*m) 0.694965

PVIFA 50.14279

PMT 1874.646

Probability Projected Return Expected Return

0.08 -6.66 -0.5328 20.34965

0.19 2.66 0.5054 8.349292

0.49 10.44 5.1156 0.649152

0.16 14.99 2.3984 5.200224

0.08 22.53 1.8024 14.02593

9.289 48.57424

6.97