07Time Value OF Money
1. Callaway, Inc. needs $2.3 million 6 years from now to purchase a machine. Currently, the firm has some extra
cash and would like to establish a savings account for this purpose. The account pays 4 percent interest,
compounded annually. How much money must the company deposit today to fully fund the machine purchase?
2. You need $20,000 in cash to buy a car 5 years from today. You expect to earn 6.5 percent, compounded
annually, on your savings. How much do you need to deposit today if this is the only money you save for this
purpose?
3. Your firm has been told that it needs $100,000 today to fund a $150,000 expansion project 8 years from now.
What rate of interest was used in the present value computation?
4. Twenty years ago, you deposited $1,000 into an account. Fifteen years ago, you added an additional $3,000 to
your account. You earned 6 percent, compounded annually, for the first 5 years and 10 percent, compounded
annually, for the last 15 years. How much money do you have in your account today?
5. What is the future value of $4,900 invested for 8 years at 7 percent compounded annually?
6.You plan to make six equal annual deposits of $5,000 with the first deposit will be made one year from now.
Your bank currently offers two options for savings accounts:
Account A:
stated annual rate of 3% with semi-annual compounding
Account B: stated annual rate of 2.8% with daily compounding
a)
Which account would you choose?
Why?
b)
If you keep the deposits in the chosen account for 20 years, how much will it have grown into?
c)
If you hope to start withdrawing $3,000 a year beginning at the 21
st
year, how many years will you
be able to receive these payments if the interest rate is 5% compounded annually?
7.Your brother plans to enter university next year and asks for your insight on his plan to borrow the costs.
To
cover his costs, he expects the first year will require a loan of $25,000, the following two years will each cost
$20,000, and that the final year will cost $30,000.
He anticipates being hired immediately upon graduation and
then taking 15 years to pay off the loans.
Assume a 4% rate of interest while in school, which will rise to 6%
upon graduation (compounds monthly).
a)
What is the value of his student loan upon graduation?
b)
What monthly payment would he have to make?
c)
Like most student loans, the rate is variable but the payment is fixed once the loan enters re-payment.
If
the interest rate on the debt rises to 8% exactly 5 years after he graduates, how much longer will it take to pay
off the debt?
8. Which of the following provides the greatest annual interest?
A) 10% compounded annually B) 9.5% compounded monthly
C) 9% compounded quarterly D) 8.5% compounded daily
9.
To compound $100 quarterly for 20 years at 8%, we must use:
A) 40 periods at 4%. B) 5 periods at 12%. C) 10 periods at 4%. D) 80 periods at 2%.