EXAMPLE 1 Simple Interest

Interest is the money earned on a savings account or other fund. Suppose that you deposit $1000 in an account that “pays interest at a rate of 10% annually.” (This is an unrealistic rate, particularly in this era of very low interest rates. We use it solely because it makes the calculations easy.) Assuming that you make no other deposits or withdrawals, how much is in the account after 5 years?

The $1000 is the principal, the initial balance of the account. At the end of one year, interest is added. The amount of interest is 10% of the principal, or

So the balance at the beginning of the second year is . We express an interest rate either as a percentage or as a decimal fraction. “Percent” means “per 100,” so you can think of the symbol “%” as standing for “1 per 100” or . So to convert from a percentage to a decimal fraction, divide the percentage by 100 by moving the decimal point two places to the left. An interest rate of 10% is 10/100 or 0.10; an interest rate as a decimal number (such as 0.10) is 100r% (10%). (Caution: A common error in using the formulas in this chapter is to forget to express the percentage as a decimal; for example, for , don’t substitute 5 for the in the formula, but instead substitute 0.05.)

With simple interest, interest is paid only on the original balance, no matter how much interest has accumulated. At the end of the first year, the account will contain $1100. But at the end of the second year, you again receive only $100; so at the beginning of the third year, the account contains $1200. In fact, at the end of each year, you receive just $100 in interest, amounting to a final balance of $1500 at the end of the fifth year.