CP

that the biggest increases in FV and EAR occur when compounding goes from annual

to semiannual, and that moving from monthly to daily compounding has a relatively

small impact. Although Table 2-1 shows daily compounding as the smallest interval, it

is possible to compound even more frequently. At the limit, one can have continuous

compounding.This is explained in the Chapter 2 Web Extension, available on the

textbook’s web site.

Define the nominal (or quoted) rate, the periodic rate, and the effective annual

rate.

Which rate should be shown on time lines and used in calculations?

What changes must you make in your calculations to determine the future value

of an amount that is being compounded at 8 percent semiannually versus one

being compounded annually at 8 percent?

Why is semiannual compounding better than annual compounding from a saver’s

standpoint? What about a borrower’s standpoint?

Fractional Time Periods

In all the examples used thus far in the chapter, we have assumed that payments occur

at either the beginning or the end of periods, but not at some date withina period.

However, we often encounter situations that require compounding or discounting

over fractional periods. For example, suppose you deposited $100 in a bank that adds

interest to your account daily, that is, uses daily compounding, and pays a nominal rate

Fractional Time Periods 87

Using the Internet for Personal Financial Planning

People continually face important financial decisions that
require an understanding of the time value of money. Should
we buy or lease a car? How much and how soon do we need
to save for our children’s education? What size house can we
afford? Should we refinance our home mortgage? How
much must we save in order to retire comfortably?
The answers to these questions are often complicated,
and they depend on a number of factors, such as housing and
education costs, interest rates, inflation, expected family in-
come, and stock market returns. Hopefully, after completing
this chapter, you will have a better idea of how to answer
such questions. Moreover, there are a number of online re-
sources available to help with financial planning.
A good place to start is http://www.smartmoney.com.
Smartmoneyis a personal finance magazine produced by the
publishers of The Wall Street Journal.If you go to Smart-
money’s web site you will find a section entitled “Tools.” This

section has a number of financial calculators, spreadsheets,

and descriptive materials that cover a wide range of personal

finance issues.

Another good place to look is Quicken’s web site,

http://www.quicken.com.Here you will find several inter-

esting sections that deal with a variety of personal finance is-

sues. Within these sections you will find background articles

plus spreadsheets and calculators that you can use to analyze

your own situation.

Finally, http://www.financialengines.com is a great

place to visit if you are focusing specifically on retirement

planning. This web site, developed by Nobel Prize–winning

financial economist William Sharpe, considers a wide range

of alternative scenarios that might occur. This approach,

which enables you to see a full range of potential outcomes,

is much better than some of the more basic online calcula-

tors that give you simple answers to complicated questions.

Time Value of Money 85