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How much interest will your savings account earn in the next year? What difference does it make how the interest is calculated? How much should you save for a comfortable retirement in the face of inflation? In this chapter, we consider such questions and show how the underlying mathematical models also help explain the recent mortgage and bank crisis and the effect of interest-rate changes on stock prices.

We look at two ways that money can grow at interest: simple interest, which is arithmetic (or linear) growth, and compound interest, which is geometric (or exponential) growth. A compound interest rate can be converted to an equivalent simple interest rate, called the effective rate, which for a period of a year is known as the annual percentage yield (APY). That is the rate that must be advertised by banks that try to attract your savings. Interest can be compounded any number of times in a year; but there is a limit to how much can be realized, even with compounding infinitely often (known as continuous compounding).

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For regular deposits to a savings account-to save up for a car, the down payment on a house, or other purchases-there is a formula that relates the size of the regular deposit, the interest rate, the amount to be accumulated, and the time to realize it. We derive this formula and show you how to use it to find any of the quantities if you know the others.

However, dollars saved may lose value due to inflation, so we show how to take inflation into account in your savings plans. Inflation, a “decay” of dollars, is usually expressed in terms of the Consumer Price Index (CPI). You learn how to convert from the CPI to the rate of inflation and how to determine the real rate of growth of an investment under inflation.

This chapter and the next encompass the world of savings and loans that you will experience in your lifetime, ranging from your parents (and you) saving for your college education to making time payments on a car or home loan to saving-and withdrawing savings-for retirement.