64 INTERESTAND EQUIVALENCE
future. This chapter will provide the methods for comparing the alternatives to determine
which motor is preferred.Time Value of Money
We often find that the monetary consequences of any alternative occur over a substantial
period of time-say, a year or more. When monetary consequencesoccur in a short period
of time, we simply add up the various sums of money and obtain a net result. But can we
treat money this way when the time span is greater?
Which would you prefer, $100 cash today or the assurance of receiving $100 a year
from now? You might decide you would prefer the $100 now because that is one way to be
certain of receiving it. But suppose you were convinced that you would receive the $100
one year hence. Now what would be your answer? A little thought should convinceyou that
itstillwould be more desirable to receive the $100 now.If you had the money now,rather
than a year hence, you would have the use of it for an extra year. And if you had no current
use for $100, you could let someone else use it.
Money is quite a valuable asset-so valuable that people are willing to pay to have
money available for their use. Money can be rented in roughly the same way one rents an
apartment, only with money,the charge is calledinterestinstead of rent. The importance
of interest is demonstrated by banks and savings institutions continuously offering to pay
for the use of people's money,to pay interest.
If the current interest rate is 9% per year, and you put $100 into the bank for one year,
how much will you receive back at the end of the year? You will receive your original
$100 together with $9 interest, for a total of $109. This example demonstrates the time
preference for money: we would rather have $100 today than the assured promise of $100
one year hence; but we might well consider leaving the $100 in a bank if we knew it would
be worth $109 one year hence. This is because there is atime value of moneyin the form
of the willingness of banks, businesses, and people to pay interest for the use of various
sums.Simple Interest
Simple interestis interest that is computed only on the original sum and not on accrued
interest. Thus if you were to loan a present sum of moneyPto someone at a simple annual
interest ratei(stated as a decimal)for a period ofnyears, the amount of interest you would
receive from the loan would be:Total interest earned=P xixn=Pin (3-1)
At the end ofnyears the amount of money due you,F,would equal the amount of the loan.
Pplus the total interest earned. That is, the amount of money due at the end of the loan
would beF=P+Pin (3-2)
orF= PO +in).