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Chapter 5
The Time Value of Money
Self Study Problems
5.1
Amit Patel is planning to invest $10,000 in a bank certificate of deposit (CD) for five
years. The CD will pay interest of 9 percent. What is the future value of Amit’s
investment?
Solution
:
Present value of the investment = PV = $10,000
Interest rate on CD =
i
= 9%
No. of years =
n
= 5.
0
1
2
3
4
5
├───┼───┼───┼────┼───┤
-$10,000
FV=?
$15,386.24
=
+
=
+
=
5
)
09
.
0
1
(
000
,
10
$
)
1
(
PV
FV
n
i
5.2
Megan Gaumer expects to need $50,000 as a down payment on a house in six years. How
much does she need to invest today in an account paying 7.25 percent?
Solution
:
Amount Megan will need in 6 years = FV
6
= $50,000
No. of years
=
n
= 6
Interest rate on investment =
i
= 7.25%
Amount needed to be invested now = PV = ?
0
1
2
3
4
5
6
├───┼───┼───┼────┼───┼───┤
PV = ?
FV = $50,000
$32,853.85
=
+
=
+
=
6
)
0725
.
0
1
(
000
,
50
$
)
1
(
FV
PV
n
n
i

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5.3
Kelly Martin has $10,000 that she can deposit into a savings account for five years. Bank
A pays compounds interest annually, Bank B twice a year, and Bank C quarterly. Each
bank has a stated interest rate of 4 percent. What amount would Kelly have at the end of
the fifth year if she left all the interest paid on the deposit in each bank?
Solution
:
Present value = PV = $10,000
No. of years =
n
= 5
Interest rate =
i
= 4%
Compound period
m
:
A = 1
B = 2
C = 4
Amount at the end of 5 years = FV
5
= ?
0
1
2
3
4
5
├───┼───┼───┼────┼───┤
-$10,000
FV = ?
A:
FVn = PV x (1 +
i
/
m
)
m x n
FV
5
= 10,000 x (1 + 0.04/1)
1x5
FV
5
=
$12,166.53
B:
FV
5
= 10,000 x (1 + 0.04/2)
2x5
FV
5
=
$12,189.94
C:
FV
5
= 10,000 x (1 + 0.04/4)
4x5
FV
5
=
$12,201.90
5.4
You have an opportunity to invest $2,500 today and receive $3,000 in three years. What
will be the return on your investment?
Solution
:
Investment today = PV = $2,500
Amount to be received back = FV
3
= $3,000
Time of investment =
n
= 3
Return on the investment =
i
= ?
FV
n
= PV (1 +
i
)
n
$3,000 = $2,500 (1 +
i
)
3
$3,000/$2,500 = (1 +
i
)
3
i
= 6.27%
5.5
Emily Smith deposits $1,200 in her bank today. If the bank pays 4 percent simple
interest, how much money will she have at the end of five years? What if the bank pays
compound interest? How much of the earnings will be interest on interest?
Solution
:

3
Deposit today = PV = $1,200
Interest rate =
i
= 4%
No. of years =
n
= 5
Amount to be received back = FV
5
= ?
a.
Future value with simple interest
Simple interest per year = $1,200 (1.04) = $48.00
Simple interest for 5 years = $48 x 5 = $240.00
FV
5
= $1,200 + $240 = $1,440.00
b.
Future value with compound interest
FV
5
= $1,200 (1 + 0.04)
5
FV
5
= $1,459.98
Simple interest = ($1,440 – $1,200) x 5 =
$240
Interest-on-interest = $1,459.98 – $1,200 – $240 =
$19.98

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Critical Thinking Questions
5.1
Explain the phrase “a dollar today is worth more than a dollar tomorrow.”
The implication is that if one was to receive a dollar today instead of in the future, the

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