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Solution 7/16/2015
Chapter: 4 Time Value of Money
Problem: 35
Inputs: PV = 1000
I/YR = 10%
N = 5
Formula: FV = PV(1+I)^N = 1,610.51$
Wizard (FV): $1,610.51
a. Find the FV of $1,000 invested to earn 10% annually 5 years from now. Answer this question
by using a math formula and also by using the Excel function wizard.
Note: When you use the wizard and fill in the menu items, the result is the formula you see on the
formula line if you click on cell E12. Put the pointer on E12 and then click the function wizard (fx) to see
the completed menu. Also, it is generally easiest to fill in the wizard menus by clicking on one of the
To create the graph, first select the range C33:E38. Then click the chart wizard. Then follow the menu.
It is easy to make a chart, but a lot of detailed steps are involved to format it so that it's "pretty." Pretty
charts are generally not necessary to get the picture, though. Note that as the last item in the chart
menu you are asked if you want to put the chart on the worksheet or on a separate tab. This is a matter
of taste. We put the chart below on the spreadsheet so we could see how changes in the data lead to
Inputs: FV = 1000
I/YR = 10%
N = 5
Formula: PV = FV/(1+I)^N = 620.92$
Wizard (PV): 620.92$
Inputs: PV = -1000
FV = 2000
I/YR = ?
N = 5
Wizard (Rate): 14.87%
the security provide?
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.
Note: In the wizard's menu, use zero for Pmt because there are no periodic payments. Also, set the FV
with a negative sign so that the PV will appear as a positive number.
Note: Use zero for Pmt since there are no periodic payments. Note that the PV is given a negative sign
because it is an outflow (cost to buy the security). Also, note that you must scroll down the menu to
complete the inputs.
$0
$500
$1,000
$1,500
$2,000
$2,500
$3,000
012345
Future Value
Years
FV as Function of Time and Rate
0%
5%
10%
Inputs: PMT = 1,000$
N = 5
I/YR = 15%
PV: Use function wizard (PV) PV = -$3,352.16
FV: Use function wizard (FV) FV = -$6,742.38
N = 510
Formula: FV = PV(1+I)^N = 1,610.51$ 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$
g. How would the PV and FV of the above annuity change if it were an annuity due rather than
an ordinary annuity?
f. Find the PV of an ordinary annuity that pays $1,000 at the end of each of the next 5 years if
the interest rate is 15%. Then find the FV of that same annuity.
Year Payment
1100
2200
3400
Rate = 8%
To find the PV, use the NPV function: PV = 581.59$
Year Payment x (1 + I )^(N-t) = FV
1100 1.17 116.64
2200 1.08 216.00
3400 1.00 400.00
Original amount of mortgage: 50000
Term of mortgage: 10
Interest rate: 0.08
Annual payment (use PMT function): -$7,451.47
Excel does not have a function for the sum of the future values for a set of uneven payments. Therefore,
we must find this FV by some other method. Probably the easiest procedure is to simply compound
each payment, then sum them, as is done below. Note that since the payments are received at the end
of each year, the first payment is compounded for 2 years, the second for 1 year, and the third for 0
years.
i. Find the PV and FV of an investment that makes the following end-of-year payments. The
interest rate is 8%.
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
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
10 $6,899.51 $7,451.47 $551.96 $6,899.51 $0.00
(1) Create a graph that shows how the payments are divided between interest and
principal repayment over time.
$4,000.00
$6,000.00
$8,000.00
Payments
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
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
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
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
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
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
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
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
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
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
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
100 $11,851.08 $606.64 $79.01 $527.63 $11,323.45
101 $11,323.45 $606.64 $75.49 $531.15 $10,792.30
102 $10,792.30 $606.64 $71.95 $534.69 $10,257.61
103 $10,257.61 $606.64 $68.38 $538.25 $9,719.35
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
120 $602.62 $606.64 $4.02 $602.62 $0.00
To get the dialog box, click on fx, then Financial, then FV, then OK.
