1. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 5 Percents

2. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 5.8 Percent and Problem Solving: Interest

3. Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Calculating Simple Interest Interest is the money charged for using other people’s money. When you borrow money, you pay interest. When you loan or invest money, you earn interest. The money borrowed, loaned, or invested is called the principal amount, or simply principal. Interest is normally stated in terms of a percent of the principal for a given period of time. The interest rate is the percent used in computing the interest. When interest is computed on the original principal, it is called simple interest.

4. Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Simple Interest Simple Interest = Principal · Rate · Time I = P · R · T where the rate is understood to be per year and time is in years.

5. Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the simple interest after 2 years on $500 at an interest rate of 12%. I = P · R · T I = $500 · 12% · 2 I = $500 · (0.12) · 2 I = $120 The simple interest is $120.

6. Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Total Amount Finding the Total Amount of a Loan or Investment total amount (paid or received) = principal + interest

7. Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example A company borrows $62,500 for 2 years at a simple interest of 12.5% to buy an airplane. Find the total amount paid on the loan. I = P · R · T I = $62,500 · 12.5% · 2 I = $62,500 · (0.125) · 2 I = $15,625 $62,500 + $15,625 = $78,125 The total amount paid on the loan was $78,125.

8. Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Calculating Compound Interest TermDefinition Compound Interest Computed on not only the principal, but also on the interest already earned in previous compounding periods. Compounded Annually Interest is added to the principal at the end of each year and that next year’s interest is computed on this new amount.

9. Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Compound Interest Compound Interest Formula The total amount A in an account is given by where P is the principal, r is the interest rate written as a decimal, t is the length of time in years, and n is the number of times compounded per year.

10. Martin-Gay, Developmental Mathematics, 2e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example n = 1, P = $1800 r = 2% (0.02) t = 3 years $1800 is invested at 2% interest compounded annually. Find the total amount after 3 years. The total amount at the end of 3 years was $1910.17.

11. Martin-Gay, Developmental Mathematics, 2e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Monthly Payment Finding the Monthly Payment of a Loan

12. Martin-Gay, Developmental Mathematics, 2e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example The monthly payment is about $216.54 Jim Tillman borrows $1800 for 9 months. If the interest is $148.90, find his monthly payment.