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Chapter 4
Time Value of Money
E4-2.
Finding the Future Value
Answer:
Since the interest is compounded monthly, the number of periods is 4 × 12
=
48 and the
monthly interest rate is 1/12th of the annual rate.
FV
48
=
PV × (1
+
i)
48
where i is the monthly interest rate
i
=
0.02 ÷ 12
=
0.00166667
FV
48
=
($1,260
+
$975) × (1
+
0.00166667)
48
FV
48
=
($1,260
+
$975) × (1
+
0.00166667)
48
FV
48
=
($2,235) × 1.083215
=
$2,420.99
If using a financial calculator, set the calculator to 12 compounding periods per year and input
the following:
PV
=
$2,235
I/year
=
2
N
=
48 (months)
Solve for FV
FV
=
$2,420.99
Note:
Not all financial calculators work in the same manner. Some require the user to use the
CPT (Compute) button. Others require the user to calculate the monthly interest rate and input
that amount rather than the annual rate. The steps shown in the solution manual will be the
inputs needed to use the Hewlett Packard 10B or 10BII models.
If using a spreadsheet, the solution is:
Column
A
Column B
Cell 1
Future Value of a Single Amount
Cell 2
Present Value
$2,235
Cell 3
Interest rate, pct per year compounded monthly
=
2/12
Cell 4
Number of months
=
4
×
12
Cell 5
Future Value
=
FV(B3,B4,0,–B2,0)
Cell B5
=
$2,420.99
E4-6.
Determining Deposits Needed to Accumulate a Future Sum
Answer:
The financial calculator input is as follows:
FV
=
–$150,000
N
=
18
I
=
6%
Solve for PMT.
PMT
=
$4,853.48

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*Sign up* Chapter 4
Time Value of Money
74
±
Solutions to Problems
P4-2.
LG 2: Future Value Calculation: FV
n
=
PV
×
(1
+
i)
n
Basic
Case
A
FVIF
12%,2 periods
=
(1
+
0.12)
2
=
1.254
B
FVIF
6%,3 periods
=
(1
+
0.06)
3
=
1.191
C
FVIF
9%,2 periods
=
(1
+
0.09)
2
=
1.188
D
FVIF
3%,4 periods
=
(1
+
0.03)
4
=
1.126
P4-6.
LG 2: Time Value
Challenge
(a)
(
1)
FV
5
=
PV
×
(FVIF
2%,5
)
(2) FV
5
=
PV
×
(FVIF
4%,5
)
FV
5
=
$14,000
×
(1.104)
FV
5
=
$14,000
×
(1.217)
FV
5
=
$15,456.00
FV
5
=
$17,038.00
Calculator solution: $15,457.13
Calculator solution: $17,033.14
(b) The car will cost $1,582 more with a 4% inflation rate than an inflation rate of 2%. This
increase is 10.2% more ($1,582
÷
$15,456) than would be paid with only a 2% rate of
inflation.
P4-8.
LG 2: Time Value: FV
n
=
PV
×
FVIF
i%,n
Challenge
(a) $15,000
=
$10,200
×
FVIF
i%,5
(b) $15,000
=
$8,150
×
FVIF
i%,5
FVIF
i%,5
=
$15,000
÷
$10,200
=
1.471
FVIF
i%,5
=
$15,000
÷
$8,150
=
1.840
8%
<
i
<
9%
12%
<
i
<
13%
Calculator Solution: 8.02%
Calculator Solution: 12.98%
(c) $15,000
=
$7,150
×
FVIF
i%,5
FVIF
i%,5
=
$15,000
÷
$7,150
=
2.098
15%
<
i
<
16%
Calculator Solution: 15.97%
P4-10.
LG 2: Present Value Calculation:
n
)
i
1
(
1
PVIF
+
=
Basic
Case
A
PVIF
=
1
÷
(1
+
0.02)
4
=
0.9238
B
PVIF
=
1
÷
(1
+
0.10)
2
=
0.8264
C
PVIF
=
1
÷
(1
+
0.05)
3
=
0.8638
D
PVIF
=
1
÷
(1
+
0.13)
2
=
0.7831
P4-12.
LG 2: Present Value Concept: PV
n
=
FV
n
×
(PVIF
i%,n
)

Chapter 4
Time Value of Money
75
Intermediate
(a) PV
=
FV
6
×
(PVIF
12%,6
)
(b)
PV
=
FV
6
×
(PVIF
12%,6
)
PV
=
$6,000
×
(.507)
PV
=
$6,000
×
(0.507)
PV
=
$3,042.00
PV
=
$3,042.00
Calculator solution: $3,039.79
Calculator solution: $3,039.79
(c)
PV
=
FV
6
×
(PVIF
12%,6
)
PV
=
$6,000
×
(0.507)
PV
=
$3,042.00
Calculator solution: $3,039.79
(d)
The answer to all three parts are the same. In each case the same questions is being asked but
in a different way.
P4-14.
LG 2: Time Value: PV
=
FV
n
×
(PVIF
i%,n
)
Intermediate
PV
=
$100
×
(PVIF
8%,6
)
PV
=
$100
×
(0.630)
PV
=
$63.00
Calculator solution: $63.02
P4-16.
LG 2: Time Value Comparisons of Lump Sums: PV
=
FV
n
×
(PVIF
i%,n
)
Intermediate
(
a)
A
PV
=
$28,500
×
(PVIF
11%,3
)
B
PV
=
$54,000
×
(PVIF
11%,9
)
PV
=
$28,500
×
(0.731)
PV
=
$54,000
×
(0.391)
PV
=
$20,833.50
PV
=
$21,114.00
Calculator solution: $20,838.95
Calculator solution: $21,109.94
C
PV
=
$160,000
×
(PVIF
11%,20
)
PV
=
$160,000
×
(0.124)
PV
=
$19,840.00
Calculator solution: $19,845.43
(b)
Alternatives A and B are both worth greater than $20,000 in term of the present value.

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