Chapter 5: The Time Value of Money
5.1
The simple interest per year is:
$5,000 × 0.07 = $350
So, after 10 years, you will have:
$350 × 10 = $3,500 in interest.
The total balance will be $5,000 + 3,500 = $8,500
With compound interest, we use the future value formula:
FV = PV(1 +r)
t
FV = $5,000(1.07)
10
= $9,835.76
The difference is:
$9,835.76 – 8,500 = $1,335.76
5.2
To find the FV of a lump sum, we use:
FV = PV(1 + r)
t
a. FV = $1,000(1.05)
10
= $1,628.89
b. FV = $1,000(1.07)
10
= $1,967.15
c. FV = $1,000(1.05)
20
= $2,653.30
d. Because interest compounds on the interest already earned, the future value in
part c is
more than twice the future value in part a. With compound interest,
future values grow
exponentially.
5.3
To find the PV of a lump sum, we use:
PV = FV / (1 + r)
t
PV = $15,451 / (1.05)
6
= $11,529.77
PV = $51,557 / (1.11)
9
= $20,154.91
PV = $886,073 / (1.16)
18
= $61,266.87
PV = $550,164 / (1.19)
23
= $10,067.28
5.4
To find the future value with continuous compounding, we use the equation:
FV = PV e
rt
a.
FV = $1,000 e
.12(5)
= $1,822.12
b.
FV = $1,000 e
.10(3)
= $1,349.86
c.
FV = $1,000 e
.05(10)
= $1,648.72
d.
FV = $1,000 e
.07(8)
= $1,750.67
Answers to End–of–Chapter Problems
B–21