Principles of Managerial Finance

CHAPTER 4 Time Value of Money 187

5.01

1250 PV

FV

CPT

I

N

 1520
4

Solution

Input Function

13. To obtain more precise estimates of interest or growth rates, interpolation—a mathematical technique for esti-
    mating unknown intermediate values—can be applied. For information on how to interpolate a more precise answer
    in this example, see the book’s home page at http://www.aw.com/gitman.

interest factor for a single amount for 4 years, PVIFi,4yrs, which is 0.822

($1,250$1,520). The interest rate in Table A–2 associated with the factor clos-

est to 0.822 for 4 years is the interest or growth rate of Ray’s cash flows. In the

row for year 4 in Table A–2, the factor for 5 percent is 0.823—almost exactly the

0.822 value. Therefore, the interest or growth rate of the given cash flows is

approximately (to the nearest whole percent) 5%.^13

Calculator Use Using the calculator, we treat the earliest value as a present

value,PV,and the latest value as a future value,FVn.(Note:Most calculators

requireeitherthePVor theFVvalue to be input as a negative number to cal-

culate an unknown interest or growth rate. That approach is used here.) Using

the inputs shown at the left, you will find the interest or growth rate to be

5.01%, which is consistent with, but more precise than, the value found using

Table A–2.

Spreadsheet Use The interest or growth rate for the series of cash flows also can

be calculated as shown on the following Excel spreadsheet.

Another type of interest-rate problem involves finding the interest rate asso-

ciated with an annuity,or equal-payment loan.

EXAMPLE Jan Jacobs can borrow $2,000 to be repaid in equal annual end-of-year amounts

of $514.14 for the next 5 years. She wants to find the interest rate on this loan.

Table Use Substituting PVA 5 $2,000 and PMT$514.14 into Equation 4.26

and rearranging the equation to solve for PVIFAi,5yrs, we get

PVIFAi,5yrs3.890 (4.28)

$2,000



$514.14

PVA 5



PMT