Math in Our World Section 8.2 Simple Interest

Learning Objectives Compute simple interest and future value. Compute principal, rate, or time. Compute the true rate for a discounted loan.

Interest Interest (I ) is the fee charged for the use of money. Simple interest is a one-time percent of an amount of money.

Interest Principal (P) is the amount of money borrowed or placed into a savings account. Rate (r) is the percent of the principal paid for having money loaned, or earned for investing money. Unless indicated otherwise, rates are given as a percent for a term of 1 year. Time (t) or term is the length of time that the money is being borrowed or invested. When the rate is given as a percent per year, time has to be written in years. Future value (A) is the amount of the loan or investment plus the interest paid or earned.

Interest Formulas for Computing Simple Interest and Final Value 1. Interest = principal x rate x time: I = Prt 2. Future value principal interest: A = P + I or A = P (1 + rt)

EXAMPLE 1 Computing Simple Interest Find the simple interest on a loan of $3,600.00 for 3 years at a rate of 8% per year.

EXAMPLE 2 Finding Future Value Find the future value for the loan in Example 1.

EXAMPLE 5 Computing Principal Phillips Health and Beauty Spa is replacing one of its workstations. The interest on a loan secured by the spa was $93.50. The money was borrowed at 5.5% simple interest for 2 years. Find the principal.

Discounted Loans Sometimes the interest on a loan is paid upfront by deducting the amount of the interest from the amount the bank gives you. This type of loan is called a discounted loan. The interest that is deducted from the amount you receive is called the discount.

EXAMPLE 9 Finding the True Rate of a Discounted Loan A student obtained a 2-year $4,000 loan for college tuition. The rate was 9% simple interest and the loan was a discounted loan. (a) Find the discount (total interest for the loan). (b) Find the amount of money the student received. (c) Find the true interest rate.