Explain what is meant by the following statement: “A dollar in hand today is
worth more than a dollar to be received next year.”
What is compounding? Explain why earning “interest on interest” is called “com-
pound interest.”
Explain the following equation: FV 1 PV INT.
Set up a time line that shows the following situation: (1) Your initial deposit is
$100. (2) The account pays 5 percent interest annually. (3) You want to know how
much money you will have at the end of three years.
Write out an equation that could be used to solve the preceding problem.
What are the five TVM (time value of money) input keys on a financial calculator?
List them (horizontally) in the proper order.
Present Value
Suppose you have some extra cash, and you have a chance to buy a low-risk secu-
rity that will pay $127.63 at the end of five years. Your local bank is currently of-
fering 5 percent interest on five-year certificates of deposit (CDs), and you re-
gard the security as being exactly as safe as a CD. The 5 percent rate is defined as
your opportunity cost rate,or the rate of return you could earn on an alterna-
tive investment of similar risk. How much should you be willing to pay for the
security?
From the future value example presented in the previous section, we saw that an
initial amount of $100 invested at 5 percent per year would be worth $127.63 at the
end of five years. As we will see in a moment, you should be indifferent between
$100 today and $127.63 at the end of five years. The $100 is defined as the present
value,or PV,of $127.63 due in five years when the opportunity cost rate is 5 per-
cent. If the price of the security were less than $100, you should buy it, because its
price would then be less than the $100 you would have to spend on a similar-risk
64 CHAPTER 2 Time Value of Money
The Power of Compound Interest
Suppose you are 26 years old and just received your MBA.
After reading the introduction to this chapter, you decide to
start investing in the stock market for your retirement. Your
goal is to have $1 million when you retire at age 65. Assum-
ing you earn a 10 percent annual rate on your stock invest-
ments, how much must you invest at the end of each year in
order to reach your goal?
The answer is $2,490.98, but this amount depends criti-
cally on the return earned on your investments. If returns
drop to 8 percent, your required annual contributions would
rise to $4,185.13, while if returns rise to 12 percent, you
would only need to put away $1,461.97 per year.
What if you are like most of us and wait until later to
worry about retirement? If you wait until age 40, you will
need to save $10,168 per year to reach your $1 million goal,
assuming you earn 10 percent, and $13,679 per year if you
earn only 8 percent. If you wait until age 50 and then earn 8
percent, the required amount will be $36,830 per year.
While $1 million may seem like a lot of money, it won’t
be when you get ready to retire. If inflation averages 5 per-
cent a year over the next 39 years, your $1 million nest egg
will be worth only $116,861 in today’s dollars. At an 8 per-
cent rate of return, and assuming you live for 20 years after
retirement, your annual retirement income in today’s dollars
would be only $11,903 before taxes. So, after celebrating
graduation and your new job, start saving!
62 Time Value of Money
