Engineering Economic Analysis

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66 INTERESTAND EQUIVALENCE

In the following table we calculate on a year-to-year basis the total dollar amount due at the end

of each year. Notice that this amount becomes the principal upon which interest is calculated in

the next year (this is the compounding eff~?t).._. ___

The total amount due at the end of the fifth year, $7347, is the amount that your friend will give

you to repay the original loan. Notice that this amount is $347 more than the amount you received

for loaning the same amount, for the same period, at simple interest. This, of course, is because

of the effect of interest being earned (by you) on top of interest.

Repaying a Debt

To better understand the mechanics of interest, let us say that $5000 is owed and is to

be repaid in 5 years, together with 8% annual interest. There are a great many ways in

which debts are repaid; for simplicity,we have selected four specificways for our example.

Table 3-1 tabulates the four plans.

In Plan 1, $1000 will be paid at the end of each year plus the interest due at the end of

the year for the use of money to that point. Thus, at the end of the first year, we will have had

the use of $5000. The interest owed is 8% x $5000=$400. The end-of-year payment is,

therefore, $1000 principalplus$400 interest, for a total payment of $1400. At the end of the

second year, another $1000 principal plus interest will be repaid on the money owed during

the year.This time the amount owedhas declined from $5000 to $4000 because of the $1000

principal payment at the end of the first year. The interest payment is 8% x $4000=$320,

making the end-of-year payment a total of $1320. As indicated in Table 3-1, the se-

ries of payments' continues each year until the loan is fully repaid at the end of the

fifth year.

Plan 2 is another way to repay $5000 in 5 years with interest at 8%. This time the.

end-of-year payment is limited to the interest due, with no principal payment. Instead, the

$5000 owed is repaid in a lump sum at the end of the fifth year. The end-of-year payment

in each of the first four years of Plan 2 is 8% x $5000=$400. The fifth year, the payment

is $400 interestplusthe $5000 principal, for a total of $5400.

Plan 3 calls for five equal end-of-year payments of $1252 each. At this point, we have

not shown how the figure of $1252 was computed (see later: Example 4-3). However, it is

Total Principal(P) Interest(I)Owed at the End Total Amount Due at the

on Which Interest is of Year n from Year n's End of Year n, New Total

Year Calculated in Year n Unpaid Total Principal Principal for Year n + 1

(^1) $5000 , $5000 x 0.08= 400 $5000 + 400= 5400
2 5400 5400 x 0.08= (^432) 5400 + 432= 5832
3 5832 5832 x 0.08= (^467) 5832 + 467= 6299
4 6299 6299 x 0.08= (^504) 6299 + 504= 6803
5 6803 6803 x 0.08= (^544) 6803 + 544= 7347