FINA 351 – Managerial Finance, Time-Value-of-Money, (Ref 4-5d)
Answer the following questions.
1.
2.
3.
Jerry invests $40,000 at a 10% annual rate in a savings account at Baker Boyer Bank. He leaves the money in the
bank without making any withdrawals for 8 years. At the end of 8 years, Jerry needs the money to pay for college
and he withdraws all of it.
A. How much did Jerry withdraw assuming the investment earned simple interest?
B.
How much did Jerry withdraw assuming the investment earned interest compounded annually?
C.
How much did Jerry withdraw assuming the investment earned interest compounded semi-annually?
Calculate how much would be in the bank after one year if you made one deposit of $100 now and left it there to
earn interest at an annual rate of 12 percent compounded:
A. annually
B.
semi-annually. (Solve using future value formulas or tables or the EAR formula)
C.
quarterly. (Solve using future value formulas or tables or the EAR formula)
D.
monthly. (Solve using the EAR formula)
E.
daily. (Solve using the EAR formula)
F.
Continuously. (Solve using the formula for continuous compounding, see notes)
G.
What are the lessons about the effect of compounding frequency?
A. Assume that on its savings accounts Blue Mtn. Credit Union offers 10.00% APR, compounded quarterly. Down
the street, Umpqua Bank promises 10.20% APR, compounded annually. UB is obviously the better deal - - or is
it? Using the EAR formula, determine which institution offers the best deal.
B. (1) What is the name of the effective rate that banks must quote on savings accounts? (2). Go the link here and
record the best APY rate on savings in the country today.
C. A credit card reports an APR of 18%. Assuming monthly payments and compounding, what is the EAR or
APY? (See Example 5.10 in your text.)
D. Assume you are desperate for money and can’t wait until your $1200 paycheck comes in three weeks (21 days).
The Cash Store in Walla Walla will give you a payday advance loan of $1000 now but will want $1200 when
you get your paycheck. Calculate the APR and EAR on this loan. See example on p. 145 in your text.
4.
Suppose that you are 19 years old today. You plan to attend graduate school when you are 25 years old and get an
MBA from Mainline State University, which will take two years. You are worried about paying the tuition, which
you estimate will be $16,000 per year (in state-tuition, after scholarships). You decide to start a college savings
fund by depositing an equal amount in the bank at the end of each of the next 6 years. At the end of years 7 and 8
you want to be able to withdraw $16,000 for tuition. You are earning 7% return compounded annually in your
investment fund and expect returns to stay the same over this period of time. How much will you need to deposit at
the end of each of the next 6 years in order to have enough to pay for the MBA program?
5.
Use Microsoft Excel to complete the problem below. At the end of Ch. 5 in your textbook is an example of using
Excel to solve this problem.
Suppose you purchased a new vehicle for $42,000. You put 10% down in cash and the balance was financed
through Bank of America. The financing terms were: a 5-year loan, with equal monthly payments at the end of each
month which include interest at 12% APR, compounded monthly. In order to see what happens to the balance of
your loan over time, you would like to have an amortization schedule. Although the bank charges a fee of $20 to
prepare an amortization schedule, having taken this class, you can prepare one yourself fairly easily on a
spreadsheet. Complete the steps below:
A. At the end of Ch. 5, there is an example of how to use Excel to prepare a loan amortization. First calculate the
monthly payment. The formula, which can be entered into any cell, is =PMT(I, N, -PV, FV, type) where: I is the
interest rate per month (.12/12); N is the number of payments (5 x 12); -PV is the beginning balance of the loan
(-37,800); FV is the future value, which is zero; and Type is 1 for annuity due and 0 for ordinary annuity. So
you would enter into any cell =PMT(.01, 60, -37800, 0, 0). This should calculate the payment amount.
B. Create column titles the same as the example at the end of Ch. 5, except replace Year with Month.
C. Enter the month number 1, the beginning balance $37,800 and the payment amount (calculated above) into the
first three cells moving right on the first row of the table. Enter the formula for interest paid by multiplying the
cell reference for beginning balance by the monthly interest rate. Enter the formula for principal paid, which is
payment amount minus interest paid. Enter the formula for ending balance, which is beginning balance minus
principal paid.
D. Repeat Step C again for the second month, with the following exceptions: for the month column, rather than
typing in 2, enter a formula which takes the previous month number cell reference and adds one to it. For the
beginning balance cell, make it equal to the cell reference for the ending balance of the month before.
E. Block and copy the second month data down so that all 60 months have been filled in. If you did it right, the
balance should be very close to zero after the 60 th payment.
F. At the bottom, sum the payment and interest paid columns to get grand totals.
6.
Repeat the steps above in #4 except change your assumptions from a 5-year loan to a 2-year loan (i.e. 24 equal
monthly payments at an interest rate of 1% per month). Right click on the bottom tab of your first Excel worksheet
(Step 4) and create a copy. After finding the new monthly payment amount, adjust the second amortization table for
24 months. Sum the total payments and interest at the bottom. Finally, answer these questions: (A) What is the
advantage of switching to a 24-month maturity? (B) What is the disadvantage of switching to a 24-month maturity?
Then submit your Excel file, with the two tabs (one for 50 payment and the other for 24 payments).