2 Learning Objectives Compute simple interest and future value. Compute principal, rate, or time.Compute the true rate for a discounted loan.
3 Interest Interest (I ) is the fee charged for the use of money. Simple interest is a one-time percent of an amount of money.
4 InterestPrincipal (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.
5 Interest Formulas for Computing Simple Interest and Final Value 1. Interest = principal x rate x time:I = Prt2. Future value principal interest:A = P + I or A = P (1 + rt)
6 EXAMPLE 1 Computing Simple Interest Find the simple interest on a loan of $3, for 3 years at a rate of 8% per year.
7 EXAMPLE 2 Finding Future Value Find the future value for the loan in Example 1.
8 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 $ The money was borrowed at 5.5% simple interest for 2 years. Find the principal.
9 Discounted LoansSometimes 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.
10 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.