Solution 12/7/2012
Chapter: 4
Problem: 35
To get the dialog box, click on fx, then Financial, then FV, then OK.
Inputs: PV = 1000
I/YR = 10%
N = 5
matter of taste. We put the chart below on the spreadsheet so we could see how changes in the data
Note that the inputs to the data table, hence to the graph, are now in the row and column heads.
Change the 20% in Cell E32 to .3 (or 30%), then to .4, then to .5, etc., to see how the table and the
a. Find the FV of $1,000 invested to earn 10% annually 5 years from now. Answer this
question by using a math formula and also by using the Excel function wizard.
b. Now create a table that shows the FV at 0%, 5%, and 20% for 0, 1, 2, 3, 4, and 5 years. Then
create a graph with years on the horizontal axis and FV on the vertical axis to display your
results.
Begin by typing in the row and column labels as shown below. We could fill in the table by inserting
formulas in all the cells, but a better way is to use an Excel data table as described in the model for
Chapter 4 (Bond Valuation). We used the data table procedure. Note that the Row Input Cell is D9
and the Column Input Cell is D10, and we set Cell B32 equal to Cell E11. Then, we selected
(highlighted) the range B32:E38, then clicked Data, Table, and filled in the menu items to complete the
table.
Formula: FV = PV(1+I)^N = 1,610.51$
Wizard (FV): $1,610.51
Note: When you use the wizard and fill in the menu items, the result is the formula you see on the
formula line if you click on cell E12. Put the pointer on E12 and then click the function wizard (fx) to
see the completed menu. Also, it is generally easiest to fill in the wizard menus by clicking on one of
the menu slots to activate the cursor and then clicking on the cell where the item is given. Then, hit
Inputs: FV = 1000
I/YR = 10%
d. A security has a cost of $1,000 and will return $2,000 after 5 years. What rate of return does the
security provide?
Inputs: PV = -1000
FV = 2000
I/YR = ?
N = 5
Wizard (Rate): 14.87%
Inputs: PV = -30
FV = 60
I/YR = growth rate 2%
N = ?
Wizard (NPER): 35.00 = Years to double.
c. Find the PV of $1,000 due in 5 years if the discount rate is 10% per year. Again, work the
problem with a formula and also by using the function wizard.
e. Suppose California’s population is 30 million people, and its population is expected to grow
by 2% per year. How long would it take for the population to double?
N = 5
Formula: PV = FV/(1+I)^N = 620.92$
Wizard (PV): 620.92$
Inputs: PMT = 1,000$
N = 5
I/YR = 15%
g. How would the PV and FV of the above annuity change if it were an annuity due rather than an
ordinary annuity?
PV annuity due = -$3,352.16 x 115% = -$3,854.98
Exactly the same adjustment is made to find the FV of the annuity due.
FV annuity due = -$6,742.38 x 115% = -$7,753.74
h. What would the FV and the PV for parts a and c be if the interest rate were 10% with
semiannual compounding rather than 10% with annual compounding?
Part a. FV with semiannual compounding: Orig. Inputs New Inputs
Inputs: PV = 1000 1000
I/YR = 10% 5%
N = 510
Formula: FV = PV(1+I)^N = 1,610.51$ 1,628.89$
Wizard (FV): 1,610.51$ 1,628.89$
Part c. PV with semiannual compounding: Orig. Inputs New Inputs
Inputs: FV = 1000 1000
I/YR = 10% 5%
N = 510
Formula: PV = FV/(1+I)^N = 620.92$ 613.91$
Wizard (PV): 620.92$ 613.91$
For the PV, each payment would be received one period sooner, hence would be discounted back one
less year. This would make the PV larger. We can find the PV of the annuity due by finding the PV of
an ordinary annuity and then multiplying it by (1 + I).
f. Find the PV of an ordinary annuity that pays $1,000 at the end of each of the next 5 years if
the interest rate is 15%. Then find the FV of that same annuity.
PV: Use function wizard (PV) PV = -$3,352.16
FV: Use function wizard (FV) FV = -$6,742.38
i. Find the PV and FV of an investment that makes the following end-of-year payments. The
interest rate is 8%.
Year Payment
1100
2200
3400
Original amount of mortgage: 50000
Term of mortgage: 10
Interest rate: 0.08
Annual payment (use PMT function): -$7,451.47
j. Suppose you bought a house and took out a mortgage for $50,000. The interest rate is 8%,
and you must amortize the loan over 10 years with equal end-of-year payments. Set up an
amortization schedule that shows the annual payments and the amount of each payment that
repays the principal and the amount that constitutes interest expense to the borrower and
interest income to the lender.
To find the PV, use the NPV function: PV = 581.59$
Year Beg. Amt. Pmt Interest Principal End. Bal.
1 $50,000.00 $7,451.47 $4,000.00 $3,451.47 $46,548.53
2 $46,548.53 $7,451.47 $3,723.88 $3,727.59 $42,820.93
(1) Create a graph that shows how the payments are divided between interest and
principal repayment over time.
(2) Suppose the loan called for 10 years of monthly payments, 120 payments in all, with
the same original amount and the same nominal interest rate. What would the
amortization schedule show now?
Now we would have a 12 × 10 = 120-payment loan at a monthly rate of .08/12 = 0.666667%.
The monthly payment would be: -$606.64
$6,000.00
$8,000.00
Breakdown of
Payments
3 $42,820.93 $7,451.47 $3,425.67 $4,025.80 $38,795.13
4 $38,795.13 $7,451.47 $3,103.61 $4,347.86 $34,447.27
5 $34,447.27 $7,451.47 $2,755.78 $4,695.69 $29,751.58
6 $29,751.58 $7,451.47 $2,380.13 $5,071.35 $24,680.23
7 $24,680.23 $7,451.47 $1,974.42 $5,477.06 $19,203.17
8 $19,203.17 $7,451.47 $1,536.25 $5,915.22 $13,287.95
9 $13,287.95 $7,451.47 $1,063.04 $6,388.44 $6,899.51
Month Beg. Amt. Pmt Interest Principal End. Bal.
1 $50,000.00 $606.64 $333.33 $273.30 $49,726.70
2 $49,726.70 $606.64 $331.51 $275.13 $49,451.57
3 $49,451.57 $606.64 $329.68 $276.96 $49,174.61
4 $49,174.61 $606.64 $327.83 $278.81 $48,895.80
5 $48,895.80 $606.64 $325.97 $280.67 $48,615.13
6 $48,615.13 $606.64 $324.10 $282.54 $48,332.60
7 $48,332.60 $606.64 $322.22 $284.42 $48,048.18
8 $48,048.18 $606.64 $320.32 $286.32 $47,761.86
26 $42,591.78 $606.64 $283.95 $322.69 $42,269.09
27 $42,269.09 $606.64 $281.79 $324.84 $41,944.25
28 $41,944.25 $606.64 $279.63 $327.01 $41,617.24
29 $41,617.24 $606.64 $277.45 $329.19 $41,288.05
30 $41,288.05 $606.64 $275.25 $331.38 $40,956.66
31 $40,956.66 $606.64 $273.04 $333.59 $40,623.07
32 $40,623.07 $606.64 $270.82 $335.82 $40,287.25
33 $40,287.25 $606.64 $268.58 $338.06 $39,949.20
34 $39,949.20 $606.64 $266.33 $340.31 $39,608.89
35 $39,608.89 $606.64 $264.06 $342.58 $39,266.31
36 $39,266.31 $606.64 $261.78 $344.86 $38,921.44
37 $38,921.44 $606.64 $259.48 $347.16 $38,574.28
38 $38,574.28 $606.64 $257.16 $349.48 $38,224.81
39 $38,224.81 $606.64 $254.83 $351.81 $37,873.00
40 $37,873.00 $606.64 $252.49 $354.15 $37,518.85
41 $37,518.85 $606.64 $250.13 $356.51 $37,162.34
42 $37,162.34 $606.64 $247.75 $358.89 $36,803.45
43 $36,803.45 $606.64 $245.36 $361.28 $36,442.17
44 $36,442.17 $606.64 $242.95 $363.69 $36,078.48
45 $36,078.48 $606.64 $240.52 $366.11 $35,712.36
46 $35,712.36 $606.64 $238.08 $368.56 $35,343.81
47 $35,343.81 $606.64 $235.63 $371.01 $34,972.79
48 $34,972.79 $606.64 $233.15 $373.49 $34,599.31
49 $34,599.31 $606.64 $230.66 $375.98 $34,223.33
50 $34,223.33 $606.64 $228.16 $378.48 $33,844.85
51 $33,844.85 $606.64 $225.63 $381.01 $33,463.84
52 $33,463.84 $606.64 $223.09 $383.55 $33,080.30
53 $33,080.30 $606.64 $220.54 $386.10 $32,694.19
54 $32,694.19 $606.64 $217.96 $388.68 $32,305.52
55 $32,305.52 $606.64 $215.37 $391.27 $31,914.25
56 $31,914.25 $606.64 $212.76 $393.88 $31,520.37
57 $31,520.37 $606.64 $210.14 $396.50 $31,123.87
58 $31,123.87 $606.64 $207.49 $399.15 $30,724.73
59 $30,724.73 $606.64 $204.83 $401.81 $30,322.92
60 $30,322.92 $606.64 $202.15 $404.49 $29,918.43
61 $29,918.43 $606.64 $199.46 $407.18 $29,511.25
62 $29,511.25 $606.64 $196.74 $409.90 $29,101.36
63 $29,101.36 $606.64 $194.01 $412.63 $28,688.73
64 $28,688.73 $606.64 $191.26 $415.38 $28,273.35
65 $28,273.35 $606.64 $188.49 $418.15 $27,855.20
66 $27,855.20 $606.64 $185.70 $420.94 $27,434.26
67 $27,434.26 $606.64 $182.90 $423.74 $27,010.52
68 $27,010.52 $606.64 $180.07 $426.57 $26,583.95
69 $26,583.95 $606.64 $177.23 $429.41 $26,154.54
70 $26,154.54 $606.64 $174.36 $432.27 $25,722.27
71 $25,722.27 $606.64 $171.48 $435.16 $25,287.11
72 $25,287.11 $606.64 $168.58 $438.06 $24,849.05
73 $24,849.05 $606.64 $165.66 $440.98 $24,408.07
74 $24,408.07 $606.64 $162.72 $443.92 $23,964.16
75 $23,964.16 $606.64 $159.76 $446.88 $23,517.28
76 $23,517.28 $606.64 $156.78 $449.86 $23,067.42
77 $23,067.42 $606.64 $153.78 $452.86 $22,614.57
78 $22,614.57 $606.64 $150.76 $455.87 $22,158.69
79 $22,158.69 $606.64 $147.72 $458.91 $21,699.78
80 $21,699.78 $606.64 $144.67 $461.97 $21,237.81
81 $21,237.81 $606.64 $141.59 $465.05 $20,772.76
82 $20,772.76 $606.64 $138.49 $468.15 $20,304.60
83 $20,304.60 $606.64 $135.36 $471.27 $19,833.33
84 $19,833.33 $606.64 $132.22 $474.42 $19,358.91
85 $19,358.91 $606.64 $129.06 $477.58 $18,881.33
86 $18,881.33 $606.64 $125.88 $480.76 $18,400.57
87 $18,400.57 $606.64 $122.67 $483.97 $17,916.60
88 $17,916.60 $606.64 $119.44 $487.19 $17,429.41
9 $47,761.86 $606.64 $318.41 $288.23 $47,473.63
10 $47,473.63 $606.64 $316.49 $290.15 $47,183.49
11 $47,183.49 $606.64 $314.56 $292.08 $46,891.41
12 $46,891.41 $606.64 $312.61 $294.03 $46,597.38
13 $46,597.38 $606.64 $310.65 $295.99 $46,301.39
14 $46,301.39 $606.64 $308.68 $297.96 $46,003.43
15 $46,003.43 $606.64 $306.69 $299.95 $45,703.48
16 $45,703.48 $606.64 $304.69 $301.95 $45,401.53
17 $45,401.53 $606.64 $302.68 $303.96 $45,097.57
18 $45,097.57 $606.64 $300.65 $305.99 $44,791.58
19 $44,791.58 $606.64 $298.61 $308.03 $44,483.55
20 $44,483.55 $606.64 $296.56 $310.08 $44,173.47
21 $44,173.47 $606.64 $294.49 $312.15 $43,861.32
22 $43,861.32 $606.64 $292.41 $314.23 $43,547.10
23 $43,547.10 $606.64 $290.31 $316.32 $43,230.77
24 $43,230.77 $606.64 $288.21 $318.43 $42,912.34
25 $42,912.34 $606.64 $286.08 $320.56 $42,591.78
89 $17,429.41 $606.64 $116.20 $490.44 $16,938.97
90 $16,938.97 $606.64 $112.93 $493.71 $16,445.26
91 $16,445.26 $606.64 $109.64 $497.00 $15,948.25
92 $15,948.25 $606.64 $106.32 $500.32 $15,447.94
93 $15,447.94 $606.64 $102.99 $503.65 $14,944.29
94 $14,944.29 $606.64 $99.63 $507.01 $14,437.28
104 $9,719.35 $606.64 $64.80 $541.84 $9,177.51
105 $9,177.51 $606.64 $61.18 $545.45 $8,632.06
106 $8,632.06 $606.64 $57.55 $549.09 $8,082.97
107 $8,082.97 $606.64 $53.89 $552.75 $7,530.21
108 $7,530.21 $606.64 $50.20 $556.44 $6,973.78
109 $6,973.78 $606.64 $46.49 $560.15 $6,413.63
110 $6,413.63 $606.64 $42.76 $563.88 $5,849.75
111 $5,849.75 $606.64 $39.00 $567.64 $5,282.11
112 $5,282.11 $606.64 $35.21 $571.42 $4,710.69
113 $4,710.69 $606.64 $31.40 $575.23 $4,135.45
114 $4,135.45 $606.64 $27.57 $579.07 $3,556.39
115 $3,556.39 $606.64 $23.71 $582.93 $2,973.46
116 $2,973.46 $606.64 $19.82 $586.81 $2,386.64
117 $2,386.64 $606.64 $15.91 $590.73 $1,795.92
118 $1,795.92 $606.64 $11.97 $594.67 $1,201.25
119 $1,201.25 $606.64 $8.01 $598.63 $602.62
95 $14,437.28 $606.64 $96.25 $510.39 $13,926.89
96 $13,926.89 $606.64 $92.85 $513.79 $13,413.10
97 $13,413.10 $606.64 $89.42 $517.22 $12,895.88
98 $12,895.88 $606.64 $85.97 $520.67 $12,375.21
99 $12,375.21 $606.64 $82.50 $524.14 $11,851.08