Build a Model Solution 11/26/2018
Chapter: 4 Time Value of Money
Problem: 35
To get the dialog box, click on fx, then Financial, then FV, then OK.
Inputs: PV =
1000
I/YR = 10%
N = 5
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
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
chart changes.
Inputs: FV = 1000
Inputs: PV =
-1000
FV = 2000
I/YR = ?
Wizard (Rate): 14.87%
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.
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?
$2,500
$3,000
Future Value
FV as Function of Time and Rate
0%
Formula: PV = FV/(1+I)^N = 620.92$
Wizard (PV): 620.92$
Inputs: PV =
-30
Inputs: PMT =
1,000$
Part a. FV with semiannual compounding: Orig. Inputs New Inputs
Inputs: PV =
1000 1000
1000 1000
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 $1,000 at the end of each of the next 5 years if
the interest rate is 15%. Then find the FV of that same annuity.
Year Payment
1
100
2
200
3
400
Rate = 8%
To find the PV, use the NPV function: PV =
581.59$
FV of PV = 732.64$
Original amount of mortgage:
50000
Term of mortgage:
10
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%.
of each year, the first payment is compounded for 2 years, the second for 1 year, and the third for 0
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
(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?
Go back to cells D184 and D185, and change the interest rate and the term to maturity to
see how the payments would change.
$6,000.00
$8,000.00
Breakdown of
Payments
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
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
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
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
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