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# Time Value of Money

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1) Calculating Annuity Present Value. An investment offers \$6,000 per year for 15 years, with the first payment occurring 1 year from now. If the required return is 8 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?

2) Calculating Annuity Future Values If you deposit \$2,000 at the end of each of the next 20 years into an account paying 7.5 percent interest, how much money will you have in the account in 20 years? How much will you have if you make deposits for 40 years?

3) EAR versus APR. Ricky Ripov's Pawn Shop charges an interest rate of 20 percent per month on loans to its customers. Like all lenders, Ricky must report an APR to consumers. What rate should the shop report? What is the effective annual rate?

4) Calculating Loan Payments. You want to buy a new sports coupe for \$52,350, and the finance office at the dealership has quoted you an 8.6 percent APR loan for 60 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?

5) Calculating Annuity Future Values. You are to make monthly deposits of \$200 into a retirement account that pays 11 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 30 years?

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#### Solution Preview

Note: For the following answers the abbreviations have the following meanings

PVIF= Present Value Interest Factor
PVIFA= Present Value Interest Factor for an Annuity
FVIF= Future Value Interest Factor
FVIFA= Future Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations
PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%
PVIF( n, r%)= =1/(1+r%)^n
FVIF( n, r%)= =(1+r%)^n
FVIFA( n, r%)= =[(1+r%)^n -1]/r%

Calculating Annuity Present Value. An investment offers \$6,000 per year for
15 years, with the first payment occurring 1 year from now. If the required return is
8 percent, what is the value of the investment? What would the value be if the
payments occurred for 40 years? For 75 years? Forever?

Here we have to find the present value of annuity

n= 15
r= 8.00%
PVIFA (15 periods, 8.% rate ) = 8.559479
Annuity= \$6,000
Therefore ...

#### Solution Summary

Time Value of Money calculations dealing with Present Value of Annuity, Future Value of Annuity, EAR versus APR, and monthly payment for a loan.

\$2.49