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CHAPTER 4 -
41
APR = 52(7.64%)
APR = 397.42%
c. Using the cash flows from the loan, we have the PVA and the annuity payments and need to find
the interest rate, so:
PVA = $68.43 = $25[{1 – [1/(1 + r)]4}/r]
Using a spreadsheet, trial and error, or a financial calculator, we find:
73. To answer this, we can diagram the perpetuity cash flows, which are: (Note, the subscripts are only to
differentiate when the cash flows begin. The cash flows are all the same amount.)
…..
C3
C2 C2
C1 C1 C1
Thus, each of the increased cash flows is a perpetuity in itself. So, we can write the cash flows
stream as:
74. Since it is only an approximation, we know the Rule of 72 is exact for only one interest rate. Using
the basic future value equation for an amount that doubles in value and solving for t, we find:
FV = PV(1 + r)t
$2 = $1(1 + r)t
ln(2) = t ln(1 + r)
t = ln(2)/ln(1 + r)
75. We are only concerned with the time it takes money to double, so the dollar amounts are irrelevant.
So, we can write the future value of a lump sum with continuously compounded interest as:
CHAPTER 4 -
43
Calculator Solutions
1.
2.
Enter
10
5%
$1,250
N
I/Y
PV
PMT
FV
3.
Enter
6
7%
$13,827
N
I/Y
PV
PMT
FV
Solve for
$9,213.51
4.
Enter
4
$189
$287
N
I/Y
PV
PMT
FV
Solve for
11.01%
5.
Enter
7%
$625
$1,104
N
I/Y
PV
PMT
FV
Solve for
8.41
Enter
12%
$810
$5,275
N
I/Y
PV
PMT
FV
Solve for
16.53
6.
Enter
6.25%
$1
$2
N
I/Y
PV
PMT
FV
Solve for
11.43
7.
8.
11.
CFo
$0
CFo
$0
CFo
$0
C01
$795
C01
$795
C01
$795
F01
1
F01
1
F01
1
12.
Enter
9
5%
$4,350
N
I/Y
PV
PMT
FV
Solve for
$30,919.02
13.
Enter
15
7%
$5,200
N
I/Y
PV
PMT
FV
15.
Enter
13.2%
12
NOM
EFF
C/Y
Solve for
14.03%
16.
Enter
17.4%
12
NOM
EFF
C/Y
Solve for
16.15%
17.
Enter
11.6%
2
NOM
EFF
C/Y
Solve for
11.94%
18. 2nd BGN 2nd SET
Enter
102.77%
52
NOM
EFF
C/Y
Solve for
176.68%
19.
20.
21.
Enter
11
8.9%
$1,000
N
I/Y
PV
PMT
FV
23. Stock account:
Enter
360
10%/12
$850
N
I/Y
PV
PMT
FV
Solve for
$1,921,414.74
CHAPTER 4 -
48
24.
25.
Enter
6
$65,000
$125,000
N
I/Y
PV
PMT
FV
28.
Enter
28
7%
$7,300
N
I/Y
PV
PMT
FV
29.
Enter
15
11%
$750
N
I/Y
PV
PMT
FV
30.
Enter
360
5.4%/12
.80($725,000)
N
I/Y
PV
PMT
FV
31.
Enter
6
1.99%/12
$12,400
N
I/Y
PV
PMT
FV
35.
Enter
20
10%
$4,700
N
I/Y
PV
PMT
FV
Solve for
$40,013.75
Enter
20
15%
$4,700
N
I/Y
PV
PMT
FV
Solve for
$29,418.86
36.
37.
38.
Enter
360
4.8%/12
$1,025
N
I/Y
PV
PMT
FV
39.
CFo
$0
C01
$1,400
F01
1
C02
$0
I = 7.1%
NPV CPT
$5,231.56
40.
CFo
$1,000,000
C01
$1,335,000
F01
1
C02
$1,670,000
I = 5.8%
41.
Enter
6.04%
12
NOM
EFF
C/Y
Solve for
6.21%
42.
Enter
3
13%
$165,000
N
I/Y
PV
PMT
FV
43.
Enter
20
6.7%
$8,500
N
I/Y
PV
PMT
FV
44.
Enter
96
6%/12
$1,940
N
I/Y
PV
PMT
FV
