Principles of Managerial Finance

182 PART 2 Important Financial Concepts

LG6

Review Questions

4–14 What effect does compounding interest more frequently than annually

have on (a) future value and (b) the effective annual rate (EAR)?Why?

4–15 How does the future value of a deposit subject to continuous compound-

ing compare to the value obtained by annual compounding?

4–16 Differentiate between a nominal annual rate and an effective annual rate

(EAR).Define annual percentage rate (APR)andannual percentage yield

(APY).

4.6 Special Applications of Time Value

Future value and present value techniques have a number of important applica-

tions in finance. We’ll study four of them in this section: (1) deposits needed to

accumulate a future sum, (2) loan amortization, (3) interest or growth rates, and

(4) finding an unknown number of periods.

Deposits Needed to Accumulate a Future Sum

Suppose you want to buy a house 5 years from now, and you estimate that an ini-

tial down payment of $20,000 will be required at that time. To accumulate the

20,000, you will wish to make equal annual end-of-year deposits into an account

paying annual interest of 6 percent. The solution to this problem is closely related

to the process of finding the future value of an annuity. You must determine what

size annuity will result in a single amount equal to $20,000 at the end of year 5.

Earlier in the chapter we found the future value of an n-year ordinary annu-

ity, FVAn,by multiplying the annual deposit, PMT,by the appropriate interest

factor, FVIFAi,n. The relationship of the three variables was defined by Equation

4.14, which is repeated here as Equation 4.24:

FVAnPMT(FVIFAi,n) (4.24)

We can find the annual deposit required to accumulateFVAndollars by solv-

ing Equation 4.24 forPMT.IsolatingPMTon the left side of the equation gives us

PMT (4.25)

Once this is done, we have only to substitute the known values of FVAnand

FVIFAi,ninto the right side of the equation to find the annual deposit required.

EXAMPLE As just stated, you want to determine the equal annual end-of-year deposits

required to accumulate $20,000 at the end of 5 years, given an interest rate

of 6%.

Table Use Table A–3 indicates that the future value interest factor for an

ordinary annuity at 6% for 5 years (FVIFA6%,5yrs) is 5.637. Substituting

FVAn



FVIFAi,n