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