Solutions to Chapter 5
The Time Value of Money
1.
a.
Future value Year 1 = Present value × (1 + r)
Interest Year 1 = Future value Year 1 – Present value
b.
Future value Year 2 = Present value × (1 + r)2
c.
Future value Year 9 = Present value × (1 + r)9
Calculator computations:
a.
Enter 1 4 –1,000
N I/Y PV PMT FV
5-+
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Education.
b.
Enter 2 4 –1,000
c.
N I/Y PV PMT FV
N I/Y PV PMT FV
2. If you earned simple interest (without compounding), then the total growth in your
5-+
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Education.
3. Since we are assuming that it is currently 2016, 116 years have passed since 1900.
a.
Future value Year (2016 – 1900) = Present value × (1 + r)(2016 – 1900)
b.
Present value = Future value / (1 + r)t
Calculator computations:
a.
Enter 116 5 –1,000
b.
N I/Y PV PMT FV
5-+
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Education.
4.
a $100 (1.08)10 = $215.89
Calculator computations:
Enter 10 8 –100
N I/Y PV PMT FV
N I/Y PV PMT FV
N I/Y PV PMT FV
5-+
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Education.
N I/Y PV PMT FV
5.
a With simple interest, you earn 4% of $1,000, or $40 each year. There is no interest on
interest. A&er 10 years, you earn total interest of $400, and your account
accumulates to $1,400.
b FV = PV × (1 + r)t
Calculator computations:
Enter 10 4 –1,000
N I/Y PV PMT FV
Solve for 1,480.24
Est time: 01–05
Simple and compound interest
5-+
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Education.
6. FV = PV × (1 + r)t
$200 = $100 × 1.06t
1.06t = 2
Calculator computations:
Enter 6 –100 200
N I/Y PV PMT FV
Solve for 11.90
Est time: 01–05
Number of time periods
7. a. FV = A$100 (1.04)113 = A$8,409.45
Calculator computations:
a.
Enter 113 4 –100
N I/Y PV PMT FV
Solve for 8,409.45
b.
5-+
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Education.
N I/Y PV PMT FV
Solve for 598,252.29
Est time: 01–05
Future value – single period
8. FV = PV × (1 + r)t
a. t = ln($1,000 / $400) / ln1.04
b. t = ln($1,000 / $400) / ln1.08
c. t = ln($1,000 / $400) / ln1.16
Calculator computations:
a.
Enter 4 –400 1,000
N I/Y PV PMT FV
b.
Enter 8 –400 1,000
5-+
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Education.
N I/Y PV PMT FV
c.
Enter 16 –400 1,000
N I/Y PV PMT FV
Solve for 6.17
Est time: 01–05
Number of time periods
9.
a The present value of the future payo. is PV = FV / (1 + r)t = $2,000/(1.06)10 =
b The present value is now equal to PV = FV / (1 + r)t = $2,000/(1.10)10 = $771.09.
Calculator computations:
a.
Enter 10 6 –2,000
N I/Y PV PMT FV
5-+
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Education.
b.
N I/Y PV PMT FV
10. You earned compound interest of 6% for 8 years and 4% for 13 years. Your $1,000 has
grown to:
11.
a. The present value of the ultimate sales price is PV = FV / (1 + r)t = $4 million/
b. The present value of the sales price is less than the purchase price of the property,
c. PV = Per-year rent × ((1 / r) – {1 / [r(1 + r)t]}) + Sales price / (1 + r)t
Calculator computations:
a.
Enter 5 8 –4,000,000
5-+
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Education.
N I/Y PV PMT FV
c.
N I/Y PV PMT FV
Est time: 06–10
Annuities
12. PV = FV / (1 + r)t
a. $100/(1.08)10 = $46.32
Calculator computations:
a.
Enter 10 8 –100
N I/Y PV PMT FV
Solve for 46.32
b.
5-+
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Education.
c.
N I/Y PV PMT FV
d.
Enter 20 4 –100
N I/Y PV PMT FV
Est time: 01–05
Annuities
13. PV = FV / (1 + r)t = $700/(1.05)5 = $548.47
Calculator computations:
5-+
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Education.
14. PV = C1 / (1 + r)1 + C2 / (1 + r)2 + C3 / (1 + r)3 = ($200/1.06) + ($400/1.062) +
15.
Present Value Years Future Value Interest Rate
a. $400 11 $684
%00.51
400
684
)11/1(
b. $183 4 $249
%00.81
183
249
)4/1(
c. $300 7 $300
%01
300
300
)7/1(
5-+
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Education.
N I/Y PV PMT FV
N I/Y PV PMT FV
Solve for 2
Est time: 06–10
Future value – single period
17. FV = PV × (1 + r)t
Calculator computations:
Enter 10 –422.41 1,000
N I/Y PV PMT FV
Solve for 9
5-+
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Education.
18.
a. PV = C1 / (1 + r)1 + C2 / (1 + r)2 + C3 / (1 + r)3
b. The PV exceeds the cost of the factory, so the investment is a:rac3ve.
Calculator computations:
CF0 = -400,000
19. PV = FVt=2 (2-year discount factor) = $1 0.92 = $0.92
20. The PV for the quarterback is the present value of a 5-year, $3 million annuity:
$3 million annuity factor (10%, 5 years) =
million 37.11$
)10.1(10.0
1
10.0
1
million 3$
5
5-+
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Education.
Calculator computations:
a.
b.
CF0 = 4,000,000
5-+
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Education.