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Math in Our World Section 8.2 Simple Interest

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**Learning Objectives Compute simple interest and future value.**

Compute principal, rate, or time. Compute the true rate for a discounted loan.

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**Interest Interest (I ) is the fee charged for the use of money.**

Simple interest is a one-time percent of an amount of money.

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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.

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**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)

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**EXAMPLE 1 Computing Simple Interest**

Find the simple interest on a loan of $3, for 3 years at a rate of 8% per year.

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**EXAMPLE 2 Finding Future Value**

Find the future value for the loan in Example 1.

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**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.

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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.

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**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.

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