The Theory of Interest - Solutions Manual
Chapter 1
1. (a) Applying formula (1.1)
A t t 2 2t 3
so that
a t
and A 0 3
A t A t 1 2
t 2t 3 .
k
A 0 3
(b) The three properties are listed on p. 2.
(1)
(2)
(3)
1
a 0 3 1.
3
1
a t 2t 2 0 for t 0,
3
so that a t i

The Theory of Interest - Solutions Manual
Chapter 7
Chapter 7
1. The maintenance expense at time t 6 is 3000 1.06 60 4255.56 . The projected
6 1
annual return at time t 6 is 30, 000 .96 24, 461.18 . Thus,
R6 24, 461.18 4255.56 $20, 206 to the nearest doll

The Theory of Interest - Solutions Manual
Chapter 5
Chapter 5
1. The quarterly interest rate is j .06 / 4 .015 . The end of the second year is the end of
the eighth quarter. There are a total of 20 installment payments, so
R
1000
a20 .015
and using the pr

The Theory of Interest - Solutions Manual
Chapter 4
Chapter 4
1. The nominal rate of interest convertible once every two years is j, so that
4
.07
1 j 1
2
and j 1.035 1 .14752.
4
The accumulated value is taken 4 years after the last payment is made, s

The Theory of Interest - Solutions Manual
Chapter 6
Chapter 6
1. (a) P 1000 1.10 10 $385.54 .
(b) P 1000 1.09 10 $422.41 .
(c) The price increase percentage is
422.41 385.54
.0956, or 9.56%.
385.54
2. The price is the present value of the accumulated val

The Theory of Interest - Solutions Manual
Chapter 8
Chapter 8
1. Let X be the total cost. The equation of value is
X&
&
10.
X a&
where j is the monthly rate of interest or a&
12 j
10 12 j
The unknown rate j can be found on a financial calculator as 3.50

The Theory of Interest - Solutions Manual
Chapter 10
Chapter 10
1. (a) We have
1000 1.095 1.0925
1
2
1.0875
3
1.08
4
5
1.07 $3976.61.
(b) The present value is greater than in Example 10.1 (1), since the lower spot rates
apply over longer periods whi

The Theory of Interest - Solutions Manual
Chapter 3
Chapter 3
1. The equation of value using a comparison date at time t 20 is
50, 000 1000 s20 Xs10 at 7%.
Thus,
50,000 1000 s20 50,000 40,995.49
X
$651.72.
s10
13.81645
2. The down payment (D) plus the am

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

The Theory of Interest - Solutions Manual
Chapter 9
Chapter 9
1. A: A direct application of formula (9.7) for an investment of X gives
A X
10
1.08 10
1.08
X
1.32539 X .
1.05 10
1.05
B: A direct application of formula (9.3a) for the same investment