The Theory of Interest - Solutions Manual
Chapter 9
106
9. (
a
) The final salary in the 25
th
year will have had 24 increases, so that we have
()
24
10,000 1.04
$25,633
to the nearest dollar.
=
(
b
) The final five-year average salary is
()()
20
21
24
10,000
1.04
1.04
1.04
$23,736 to the nearest dollar.
5
⎡⎤
++
+
=
⎣⎦
"
(
c
) The career average salary is
22
4
10,000
1
1.04
1.04
1.04
$16,658
to the nearest dollar.
25
+
+
=
"
10. The annual mortgage payment under option A is
10 .10
240,000
40,000
32,549.08.
A
R
a
−
==
The annual mortgage payment under option B is
10 .08
240,000
40,000
29,805.90.
B
R
a
−
The value of the building in 10 years is
10
240,000 1.03
322,539.93.
=
Thus, the shared appreciation mortgage will result in a profit to Lender B
( )
.50 322,539.93 240,000
41,269.97.
−=
(
a
) The present value of payments under Option A is
10 .08
40,000 32,549.08
$258,407
to the nearest dollar.
A
PV
a
=+
=
The present value of payments under Option B is
10
10 .08
40,000
29,805.90
41,269.97 1.08
$259,116
to the nearest dollar.