Problem: 35
To get the dialog box, click on fx, then Financial, then FV, then OK.
Inputs: PV =
1000
I/YR = 10%
N = 5
Formula: FV = PV(1+I)^N = 1,610.51$
Wizard (FV): $1,610.51
formula line if you click on cell E12. Put the pointer on E12 and then click the function wizard (fx) to
see the completed menu. Also, it is generally easiest to fill in the wizard menus by clicking on one of
the menu slots to activate the cursor and then clicking on the cell where the item is given. Then, hit
the tab key to move down to the next menu slot to continue filling out the dialog box.
Years (D10):
1,610.51$ 0% 5% 20%
0$1,000.00 $1,000.00 $1,000.00
1$1,000.00 $1,050.00 $1,200.00
2$1,000.00 $1,102.50 $1,440.00
3$1,000.00 $1,157.63 $1,728.00
4$1,000.00 $1,215.51 $2,073.60
5$1,000.00 $1,276.28 $2,488.32
Interest Rate (D9)
a. Find the FV of $1,000 invested to earn 10% annually 5 years from now. Answer this question
by using a math formula and also by using the Excel function wizard, fx.
b. Now create a table that shows the FV at 0%, 5%, and 20% for 0, 1, 2, 3, 4, and 5 years. Then
create a graph with years on the horizontal axis and FV on the vertical axis to display your
results.
Begin by typing in the row and column labels as shown below in C32:C34 and B33:B38. NOTE: Do not
use formulas in these cells! You must enter the actual numbers! We could fill in the table by
inserting formulas in all the cells, but a better way is to use an Excel data table (Data, What-If Analysis,
Data Table). Note that the Row Input Cell is D9 and the Column Input Cell is D10, and we set Cell B32
equal to Cell E11. Then, we selected (highlighted) the range B32:E38, then clicked Data, What-If
Analysis, Data Table, and filled in the menu items to complete the table.
Inputs: FV = 1000
Formula: PV = FV/(1+I)^N = 620.92$
Wizard (PV): 620.92$
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.
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.
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?
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: 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.
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?
$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%
Part a. FV with semiannual compounding: Orig. Inputs New Inputs
Inputs: PV =
1000 1000
Formula: FV = PV(1+I)^N = 1,610.51$ 1,628.89$
Wizard (FV): 1,610.51$ 1,628.89$
1000 1000
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?
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?
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 $1,000 at the end of each of the next 5 years if
the interest rate is 15%. Then find the FV of that same annuity.
Year Payment
1
100
200
400
Rate = 8%
received at the end of each year, the first payment is compounded for 2 years, the second for 1 year,
Year Payment x (1 + I )^(N-t) = FV
1100 1.17 116.64
2
200 1.08 216.00
3
400 1.00 400.00
Sum =
732.64$
PV =
581.59$
FV of PV = 732.64$
An alternative procedure for finding the FV would be to find the PV of the series using the NPV
function, then compound that amount, as is done below:
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.
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
all, with the same original amount and the same nominal interest rate. What
would the amortization schedule show now?
$2,000.00
$4,000.00
$6,000.00
$8,000.00
Breakdown of
Payments
Principal
Interest
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
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
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
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
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
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
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