2
next
n
2
years, and
Pk
3
n
3
for the next
n
3
years, etc.
This implies that the future value
43
under changing simple interest rates is
44
45
FV
=
P
(1 +
n
1
k
1
+
n
2
k
2
+
n
3
k
3
+ .
...)
46
47
Example 3.1
:
Suppose an account earns 15 percent simple interest per year. What would
48
the future value be of a deposit of:
49
50
(a)
$15 left for 10 years?
51
(b)
$0.15 left for 5 years?
52
(c)
$1 left for 2,000 years?
53
54
Answers
55
56
2625
.
0
$
)
5
15
.
1
(
15
.
5
,
15
.
,
15
.
)
(
FV
n
k
P
b
57
58
59
301
$
)
000
,
2
15
.
1
(
1
000
,
2
,
15
.
,
1
)
(
n
k
P
c
60
61
62
Example 3.2
: Suppose you deposit $1,000 in an account that pays simple rate of
interest.
63
What will be the future value of the account if:
64
65
(a) the annual simple interest rate is 7% for the first 5 years, 10% for the next 10 years,
66
and 12% for the last 5 years?
67
(b) 5% for the first 10 years, 10% for the next 10 years, 15% for the last 10 years?
68
69
Answers:
70
71
(a)
P
= $1,000,
k
1
=
7%,
n
1
= 5
72
k
2
= 10%,
n
2
= 10
73
k
3
= 12%,
n
3
= 5
74
FV
= $1,000(1 + .07 × 5 + .10 × 10 + .12 × 5)
75
= $1,000(2.95) = $2,950.
76
77
(b)
P
= $1,000,
k
1
=
5%,
n
1
= 10
78
5
.
37
$
)
10
15
.
1
(
15
10
,
15
.
,
15
)
(
n
k
P
a