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45.
46. PV@ t = 14: $2,350/.063 = $37,301.59
47.
APR = 2.403% 12 = 28.84%
48. Monthly rate = .10/12 = .0083; semiannual rate = (1.0083)6 – 1 = 5.11%
Enter
10
5.11%
$5,230
N
I/Y
PV
PMT
FV
Solve for
$40,178.89
49.
a.
Enter
5
7.8%
$13,250
N
I/Y
PV
PMT
FV
Solve for
$53,183.45
50. 2nd BGN 2nd SET
51. 2nd BGN 2nd SET
52. PV of college expenses:
Enter
4
7.9%
$72,000
N
I/Y
PV
PMT
FV
Solve for
$239,004.91
Cost today of oldest child’s expenses:
54. Option A:
Aftertax cash flows = Pretax cash flows(1 – tax rate)
Aftertax cash flows = $250,000(1 – .28)
Aftertax cash flows = $180,000
56.
Enter
5 × 12
6.8%/12
$17,000
N
I/Y
PV
PMT
FV
Solve for
$305.46
57. Pre-retirement APR:
Enter
11%
12
NOM
EFF
C/Y
Solve for
10.48%
Post-retirement APR:
58. PV of purchase:
Enter
36
6%/12
$22,000
N
I/Y
PV
PMT
FV
Solve for
$18,384.19
$37,000 – 18,384.19 = $18,615.81
CHAPTER 4 -
56
59.
Enter
5.7%
365
NOM
EFF
C/Y
Solve for
5.87%
CFo
$7,900,000
C01
$4,300,000
I = 5.87%
NPV CPT
60.
61.
Enter
7.4%
12
NOM
EFF
C/Y
Solve for
7.16%
CHAPTER 4 -
57
Enter
12
7.16%/12
$39,000/12
N
I/Y
PV
PMT
FV
Solve for
$40,305.70
62.
Enter
1
$9,700
$10,800
N
I/Y
PV
PMT
FV
Solve for
11.34%
63. Refundable fee: With the $2,900 application fee, you will need to borrow $302,900 to have
$300,000 after deducting the fee. Solve for the payment under these circumstances.
Enter
30 12
5.30%/12
$302,900
N
I/Y
PV
PMT
FV
Enter
5.39%
12
NOM
EFF
C/Y
CHAPTER 4 -
58
Without refundable fee: APR = 5.30%
64.
APR = 3.04% 12 = 36.54%
65. Without fee:
Enter
8.2%/12
$12,000
$250
N
I/Y
PV
PMT
FV
66. Value at Year 6:
Enter
5
11%
$500
N
I/Y
PV
PMT
FV
Solve for
$842.53
CHAPTER 4 -
59
Enter
2
11%
$800
N
I/Y
PV
PMT
FV
Solve for
$985.68
At Year 65, the value is:
Enter
59
7%
$5,695.39
N
I/Y
PV
PMT
FV
Solve for
$308,437.08
67. Effective six-month rate = (1 + Daily rate)180 – 1
Effective six-month rate = (1 + .09/360)180 – 1
Effective six-month rate = .0460 or 4.60%
Enter
40
4.60%
$1,900,000
N
I/Y
PV
PMT
FV
Solve for
$34,458,785.87
68.
CFo
$9,000
72.
a. APR = 7.1% 52 = 369.20%
Enter
369.20%
52
NOM
EFF
C/Y
Solve for
3,440.40%
Enter
397.42%
52
NOM
EFF
C/Y
Solve for
4,504.50%
APR = 17.11% 52 = 889.82%
CHAPTER 4 -
61
CHAPTER 4, APPENDIX
NET PRESENT VALUE: FIRST
PRINCIPLES OF FINANCE
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this solutions
1. The potential consumption for a borrower next year is the salary during the year, minus the repayment
of the loan and interest to fund the current consumption. The amount that must be borrowed to fund
this year’s consumption is:
Amount to borrow = $100,000 – 80,000 = $20,000
2. The potential consumption for a saver next year is the salary during the year, plus the savings from the
current year and the interest earned. The amount saved this year is:
3. Financial markets arise to facilitate borrowing and lending between individuals. By borrowing and
lending, people can adjust their pattern of consumption over time to fit their particular preferences.
4. a. The present value of labor income is the total of the maximum current consumption. So, solving
for the interest rate, we find:
$86 = $40 + $50/(1 + r)
5. a. The market interest rate must be the increase in the maximum current consumption to the
maximum consumption next year, which is:
