The Theory of Interest - Solutions Manual
104
Chapter 9
1. A:
A direct application of formula (9.7) for an investment of
X
gives
(
)
(
)
10
10
10
1.08
1.08
1.32539
.
1.05
1.05
A
X
X
X
⎛
⎞
=
=
=
⎜
⎟
⎝
⎠
B:
A direct application of formula (9.3a) for the same investment of
X
gives
1.08
1
1.028571
1.05
i
′
+
=
=
and the accumulated value is
(
)
10
1.028571
1.32539
.
B
X
X
=
=
The ratio
/
1.00.
A B
=
2. Proceeding similarly to Exercise 1 above:
(
)
10 .08
10
10 .028571
9.60496.
1.05
11.71402.
s
A
B
s
=
=
=
=
±±
±±
The ratio
/
.82.
A B
=
3.
Again applying formula (9.7) per dollar of investment
(
)
(
)
5
5
1.07
.87087
1.10
=
so that the loss of purchasing power over the five-year period is
1
.87087
.129,
or
12.9%.
−
=
4.
The question is asking for the summation of the “real” payments, which is
(
)
(
)
2
15
15 .032
1
1
1
18,000
1.032
1.032
1.032
18,000
$211,807
to the nearest dollar.
a
⎡
⎤
+
+
+
⎢
⎥
⎣
⎦
=
=
"
5. The last annuity payment is made at time
18
t
=
and the nominal rate of interest is a
level 6.3% over the entire period. The “real” rate over the last 12 years is
.063
.012
.0504.
1
1
.012
i
r
i
r
−
−
′ =
=
=
+
+

This ** preview** has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*