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The Theory of Interest  Solutions Manual
Chapter 2
1.
The quarterly interest rate is
(
29
4
.06
.015
4
4
i
j
=
=
=
and all time periods are measured in quarters. Using the end of the third year as the
comparison date
(
29
12
4
28
3000 1
2000
5000
j
X
v
v
+
+
=
+
(
29
(
29
(
29
2000 .94218
5000 .65910
3000 1.19562
$1593.00.
X
=
+

=
2.
The monthly interest rate is
(
29
12
.18
.015.
12
12
i
j
=
=
=
Using the end of the third month as the comparison date
(
29
(
29
(
29
(
29
(
29
(
29
3
2
1000 1
200 1
300 1
1000 1.04568
200 1.03023
300 1.015
$535.13.
X
j
j
j
=
+

+

+
=


=
3.
We have
5
10
5
200
500
400.94
v
v
v
+
=
(
29
10
5
5
5
.40188
.40188
or
1
2.4883.
v
v
v
i
=
=
+
=
Now using time
10
t
=
as the comparison date
(
29
(
29
(
29
(
29
10
5
2
100 1
120 1
100 2.4883
120 2.4883
$917.76.
P
i
i
=
+
+
+
=
+
=
4.
The quarterly discount rate is 1/41 and the quarterly discount factor is
1 1/ 41 40/ 41

=
. The three deposits accumulate for 24, 16, and 8 quarters,
respectively.
Thus,
(
29
(
29
(
29
(
29
24
16
8
3
5
40
40
40
28
100 1.025
1.025
1.025
41
41
41
A



=
+
+
÷
÷
÷
.
However,
1
40
1.025
41

=
÷
so that
(
29
(
29
(
29
(
29
25
19
13
28
100 1.025
1.025
1.025
$483.11
A
=
+
+
=
.
14
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Chapter 2
5.
(
a
)
At time
10
t
=
, we have
(
29
(
29
(
29
100 1 10
100 1 5
with
.05
200 1500 .05
$275.
X
i
i
i
=
+
+
+
=
=
+
=
(
b
)
At time
15
t
=
, we have
(
29
(
29
(
29
(
29
(
29
1 5
100 1 15
100 1 10
with
.05
1.25
200
2500 .05
325
X
i
i
i
i
X
+
=
+
+
+
=
=
+
=
and
325
$260
1.25
X
=
=
.
6.
The given equation of value is
(
29
(
29
1000 1.06
2000 1.04
n
n
=
so that
[
]
1.06
2
1.04
ln1.06
ln1.04
ln 2
n
n
=
÷

=
and
.693147
36.4
years
.058269 .039221
n
=
=

.
7.
The given equation of value is
(
29
(
29
(
29
(
29
(
29
(
29
2
5
2
5
2
5
3000
2000
5000
5000
3000
2000 1
5000 1
1
1
and
3000
2000 .94
5000 .94
1
.94
n
n
n
n
v
v
v
d
d
d
+
+
=
+
+

=

+

+
=
+
since
.06
d
=
. Simplifying, we have
(
29
(
29
(
29
(
29
(
29
(
29
4767.20
8669.52 .94
4767.20
.94
.54988
8669.52
ln .94
ln .54988
ln .54988
and
9.66
years.
ln .94
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This document was uploaded on 12/05/2011.
 Fall '09

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