Principles of Managerial Finance

CHAPTER 4 Time Value of Money 189

11.91

1000 PV

FV

CPT

N

I

 2500
8

Solution

Input Function

8.15

 (^4800) PMT
PV
CPT
N
I
25000
11
Solution
Input Function
Calculator Use Using the calculator, we treat the initial value as the present
value,PV,and the latest value as the future value,FVn.(Note:Most calculators
requireeitherthePVor theFVvalue to be input as a negative number to calcu-
late an unknown number of periods. That approach is used here.) Using the
inputs shown at the left, we find the number of periods to be 11.91 years,
which is consistent with, but more precise than, the value found above using
Table A–2.
Spreadsheet Use The number of years for the present value to grow to a specified
future value also can be calculated as shown on the following Excel spreadsheet.
Another type of number-of-periods problem involves finding the number of
periods associated with an annuity.Occasionally we wish to find the unknown
life, n,of an annuity, PMT,that is intended to achieve a specific objective, such as
repaying a loan of a given amount, PVAn,with a stated interest rate, i.
EXAMPLE Bill Smart can borrow $25,000 at an 11% annual interest rate; equal, annual
end-of-year payments of $4,800 are required. He wishes to determine how long it
will take to fully repay the loan. In other words, he wishes to determine how
many years, n,it will take to repay the $25,000, 11% loan, PVAn,if the pay-
ments of $4,800, PMT,are made at the end of each year.
Table Use Substituting PVAn$25,000 and PMT$4,800 into Equation 4.26
and rearranging the equation to solve PVIFA11%,n yrs,we get
PVIFA11%,n yrs5.208 (4.29)
The number of periods for an 11% interest rate associated with the annuity fac-
tor closest to 5.208 in Table A–4 is 8 years. Therefore, the number of periods
necessary to repay the loan fully is approximately (to the nearest year) 8 years.
Calculator Use (Note:Most calculators require eitherthe PVor the PMTvalue
to be input as a negative number in order to calculate an unknown number of
periods. That approach is used here.) Using the inputs shown at the left, you will
find the number of periods to be 8.15, which is consistent with the value found
using Table A–4.
$25,000



$4,800

PVAn



PMT