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CHAPTER 1
THE TIME VALUE OF MONEY
LEARNING OUTCOMES
After completing this chapter, you will be able to do the following:
interpret interest rates as required rates of return, discount rates, or opportunity
costs;
explain an interest rate as the sum of a real risk-free rate and premiums that
compensate investors for bearing distinct types of risk;
calculate and interpret the effective annual rate, given the stated annual interest
rate and the frequency of compounding;
solve time value of money problems for different frequencies of compounding;
calculate and interpret the future value (FV) and present value (PV) of a single
sum of money, an ordinary annuity, an annuity due, a perpetuity (PV only), and a
series of unequal cash flows;
demonstrate the use of a time line in modeling and solving time value of money
problems.
SUMMARY OVERVIEW
In this reading, we have explored a foundation topic in investment mathematics, the
time value of money. We have developed and reviewed the following concepts for use
in financial applications:
The interest rate, r, is the required rate of return; r is also called the discount rate
or opportunity cost.
An interest rate can be viewed as the sum of the real risk-free interest rate and a
set of premiums that compensate lenders for risk: an inflation premium, a default
risk premium, a liquidity premium, and a maturity premium.
The future value, FV, is the present value, PV, times the future value factor, (1 +
r)N.
The interest rat