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TVM question on Excel Spreadsheet

Financial Management Questions. See attached file for full problem description.

a. Find the FV of $1,000 invested to earn 10% after 5 years. Answer this question by using a
math formula and also by using the Excel function wizard.

Inputs: PV = 1000
i = 10%
n = 5
Formula: FV = PV(1+I)^n =
Wizard (FV):

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 put the pointer on cell E12. Put the pointer on E12 and then click the function
wizard (fx) to see the completed menu. Finally, it is generally easiest to fill in the wizard menus by
clicking on one of the menu slots to activate the cursor in that slot and then clicking on the input cell
where the item is given. Then, hit the tab key to move down to the next menu slot.

Experiment by changing the input values to see how quickly the output values change.

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 07model. 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.

Years (D10): Interest Rate (D9)
0% 5% 20%
0
1
2
3
4
5

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 right on the spreadsheet so we could see how changes in the data lead to
changes in the graph.

Note that the inputs to the data table, hence to the graph, are now in the row and column heads.
Change the 10% in Cell E32 to .2 (or 20%), then to .3, then to .5, etc., to see how the table and the chart
changes.

c. Find the PV of $1,000 due in 5 years if the discount rate is 10%. Again, work the problem with
a formula and also by using the function wizard.

Inputs: FV = 1000
i = 10%
n = 5
Formula: PV = FV/(1+I)^n =
Wizard (PV):

Note: In the wizard's menu, use zero for PMTS because there are no periodic payments. Also,
set the FV with a negative sign so that the PV will appear as a positive number.

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 = ?
n = 5

Wizard (Rate):

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?

Inputs: PV = -30
FV = 60
i = growth rate 2%
n = ?

Wizard (NPER): = Years to double.

f. Find the PV of an 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.

Inputs: Pmt $1,000
n 5
i 15%

PV: Use function wizard (PV) PV =

FV: Use function wizard (FV) FV =

g. How would the PV and FV of the annuity change if it were an annuity due rather than an ordinary
annuity?

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).

PV annuity due = x =

Exactly the same adjustment is made to find the FV of the annuity due.

FV annuity due = x =

h. What would the FV and the PV for problems 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 = 10% 5%
n = 5 10
Formula: FV = PV(1+I)^n =
Wizard (FV):

Part c. PV with semiannual compounding: Orig. Inputs: New Inputs:
Inputs: FV = 1000 1000
i = 10% 5%
n = 5 10
Formula: FV = FV/(1+I)^n =
Wizard (PV):

i. Find the PV and the FV of an investment that makes the following end-of-year payments. The
interest rate is 8%.

Year Payment
1 100
2 200
3 400

Rate = 8%

To find the PV, use the NPV function: PV =

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.

Year Payment x (1 + I )^(n-t) = FV
1 100 1.17 116.64
2 200 1.08 216.00
3 400 1.00 400.00

Sum =

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:

PV =
FV of PV =

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 goes to pay off the
principal and the amount that constitutes interest expense to the borrower and interest income to
the lender.

Original amount of mortgage: 50000
Term of mortgage: 10
Interest rate: 0.08

Annual payment (use PMT function):

Year Beg. Amt. Pmt Interest Principal End. Bal.
1
2
3
4
5
6
7
8
9
10

Extensions: i. Create a graph that shows how the payments are divided between interest and
principal repayment over time.

Go back to cells D184 and D185, and change the interest rate and the term to maturity to
see how the payments would change.

ii. Suppose the loan called for 10 years of monthly payments, 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:

Month Beg. Amt. Pmt Interest Principal End. Bal.
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Answers TVM question on Excel Spreadsheet

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