Engineering Economic Analysis

Time Value of Money 67

(a)

TABLE3-1 Four Plans for Repayment of $5000 in 5 Years with Interestat 8%

(e) (f)

Total

End-of-Year

Payment

(b)

Amount Owed

at Beginning of

Year

(c)

Interest Owed for

That-Year,

8% x (b)

(d)

Total Owed at

End of Year,

Year (b) + (c)

Principal

Payment

Plan 1: At end of each year pay $1000 principalplusinterestdue.

1 $5000 $ 400 $5400

2 4000 320 4320

3 3000 240 3240

4 2000 160 2160

5 1000 80 1080

$1200

$1000

1000

1000

1000

1000

$5000

$1400

1320

1240

1160

1080

$6200

Plan 2: Pay interest due at end of each year and principalat end of 5 years.

1 $5000 $ 400 $5400 $

2 5000 400 5400

3 5000 400 5400

4 5000 400 5400

5 5000 400 5400

$2000

o

o

o

o

5000

$5000

$ 400

400

400

400

5400

$7000

Plan 3: Pay in five equal end-of-yearpayments.

1 $5000 $ 400

2 4148 331

3 3227 258

4 2233 178

5 1159 93

$1260

$5400

4479

3485

2411

1252

$ 852

921

994

1074

1159

$5000

$1252*

1252

1252

1252

1252

$6260

Plan 4: Pay principal and interest in one payment at end of 5 years.
1 $5000 $ 400 $5400
2 5400 432 5832
3 5832 467 6299
4 6299 504 6803
5 6803 544 7347
$2347

$ 0

o

o

o

5000

$5000

$ 0

o

o

o

7347

$7347

*The exact value is $1252.28, which has been rounded to an even dollar amount.

clear that there is some equal end-of-year amount that would repay the loan. By following
the computations in Table 3-1, we see that this series of five payments of $1252 repays a
$5000 debt in 5 years with interest at 8%.
Plan 4 is still another method of repaying the $5000 debt. In this plan, no payment is
made until the end of the fifth year when the loan is completely repaid. Note what happens
at the end of the first year: the interest due for the first year-8% x $5000=$400-is not
paid; instead, it is added to the debt. At the second year, then, the debt has increased to
$5400. The second year interest is thus 8% x $5400=$432. This amount, again unpaid, is