Principles of Managerial Finance

188 PART 2 Important Financial Concepts

9.00

514.14 PMT

PV

CPT

I

N

 2000

5

Solution

Input Function

The interest rate for 5 years associated with the annuity factor closest to 3.890 in

Table A–4 is 9%. Therefore, the interest rate on the loan is approximately (to the

nearest whole percent) 9%.

Calculator Use (Note:Most calculators require eitherthe PMTor the PVvalue

to be input as a negative number in order to calculate an unknown interest rate

on an equal-payment loan. That approach is used here.) Using the inputs shown

at the left, you will find the interest rate to be 9.00%, which is consistent with the

value found using Table A–4.

Spreadsheet Use The interest or growth rate for the annuity also can be calcu-

lated as shown on the following Excel spreadsheet.

Finding an Unknown Number of Periods

Sometimes it is necessary to calculate the number of time periods needed to gen-

erate a given amount of cash flow from an initial amount. Here we briefly con-

sider this calculation for both single amounts and annuities. This simplest case is

when a person wishes to determine the number of periods, n,it will take for an

initial deposit, PV,to grow to a specified future amount, FVn,given a stated

interest rate, i.

EXAMPLE Ann Bates wishes to determine the number of years it will take for her initial

$1,000 deposit, earning 8% annual interest, to grow to equal $2,500. Simply

stated, at an 8% annual rate of interest, how many years, n,will it take for Ann’s

$1,000, PV,to grow to $2,500, FVn?

Table Use In a manner similar to our approach above to finding an unknown

interest or growth rate in a series of cash flows, we begin by dividing the amount

deposited in the earliest year by the amount received in the latest year. This

results in the present value interest factor for 8% andnyears,PVIF8%,n,which is

0.400 ($1,000$2,500). The number of years (periods) in Table A–2 associated

with the factor closest to 0.400 for an 8% interest rate is the number of years

required for $1,000 to grow into $2,500 at 8%. In the 8% column of Table A–2,

the factor for 12 years is 0.397—almost exactly the 0.400 value. Therefore, the

number of years necessary for the $1,000 to grow to a future value of $2,500 at

8% is approximately (to the nearest year) 12.