Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require
multiple steps. Due to space and readability constraints, when these intermediate steps are
included in these solutions, rounding may appear to have occurred. However, the final answer
for each problem is found without rounding during any step in the problem.
CHAPTER # 5
1.
The simple interest per year is:
$5,000 × .06 = $300
So after 10 years you will have:
$300 × 10 = $3,000 in interest.
The total balance will be $5,000 + 3,000 = $8,000
With compound interest we use the future value formula:
FV = PV (1 +r)
t
FV = $5,000(1.06)
10
= $8,954.24
The difference is:
$8,954.24 – 8,000 = $954.24
3.
To find the PV of a lump sum, we use:
PV = FV / (1 +
r)
t
PV = $15,451 / (1.04)
6
= $12,211.15
PV = $51,557 / (1.11)
7
= $24,832.86
PV = $886,073 / (1.20)
23
= $13,375.22
PV = $550,164 / (1.13)
18
= $60,964.94
4.
To answer this question, we can use either the FV or the PV formula. Both will give the same
answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 +
r
)
t
Solving for
r
, we get:
r
= (FV / PV)
1 /
t
– 1
FV = $307 = $240(1 +
r
)
2
;
r
= ($307 / $240)
1/2
– 1 = 13.10%
FV = $896 = $360(1 +
r
)
10
;
r
= ($896 / $360)
1/10
– 1 = 9.55%
FV = $174,384 = $39,000(1 +
r
)
15
;
r
= ($174,384 / $39,000)
1/15
– 1 = 10.50%
FV = $483,500 = $38,261(1 +
r
)
30
;
r
= ($483,500 / $38,261)
1/30
– 1 = 8.82%
10.
To find the PV of a lump sum, we use:
PV = FV / (1 +
r)
t
PV = $700,000,000 / (1.085)
20
= $136,931,471.85
11.
To find the PV of a lump sum, we use:
PV = FV / (1 +
r)
t
PV = $1,000,000 / (1.09)
80
= $1,013.63
14.
To find the PV of a lump sum, we use:
PV = FV / (1 +
r)
t
PV = $485,000 / (1.2590)
67
= $0.10

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