1. Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.2, Slide 1 Consumer Mathematics The Mathematics of Everyday Life 8

2. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.2, Slide 2 Interest 8.2 Understand the simple interest formula. Use the compound interest formula to find future value. Solve the compound interest formula for different unknowns, such as the present value, length, and interest rate of a loan.

3. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 3 Simple Interest Interest is the money that one person (a borrower) pays to another (a lender) to use the lender’s money. The amount you deposit in a bank account is called the principal. The bank specifies an interest rate for that account as a percentage of your deposit.

4. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 4 Simple Interest

5. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 5 Simple Interest Example: $500 is deposited in a bank account paying 6% simple interest, how much interest will the deposit earn in 4 years? Solution: P = $500 (principal) r = 0.06 (rate) t = 4 (time)

6. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 6 Simple Interest To find the amount that will be in your account at some time in the future, called the future value (or sometimes called the future amount) we add the principal and the interest earned. We will represent future value by A.

7. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 7 Simple Interest

8. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 8 Simple Interest Example: $1,000 is deposited in a bank account paying 3% annual interest for 6 years. Compute the future value of this account. Solution: We see that P = 1,000, r = 0.03, and t = 6.

9. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 9 Simple Interest Example: $2,500 is needed in 2 years for a purchase. A bank offers a certificate of deposit (CD) that pays 4% annual interest computed using simple interest. How much must be put in this CD now to have the necessary money in 2 years? (continued on next slide)

10. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 10 Simple Interest Solution: We see that A = 2,500, r = 0.04, and t = 2.

11. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 11 Compound Interest Interest that is paid on principal plus previously earned interest is called compound interest. If the interest is added yearly, we say that the interest is compounded annually. If the interest is added every three months, we say the interest is compounded quarterly.

12. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 12 Compound Interest Example: $2,000 is deposited for 3 years in a bank account that pays 10% annual interest, compounded annually. How much will be in the account at the end of 3 years? Solution: Calculations, one year at a time, are in the table.

13. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 13 Compound Interest For annual compounding:

14. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 14 Solving for Unknowns in the Compound Interest Formula

15. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 15 Example: An item is $3,500 with no payments due for 6 months. Although no payments are made, the dealer is not loaning the money for 6 months for nothing. $3,500 was borrowed and, in 6 months, the payments will be based upon that fact. If the interest rate is 12%, compounded monthly, what interest will accumulate on the purchase over the next 6 months? (continued on next slide) Solving for Unknowns in the Compound Interest Formula

16. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 16 Solution: We see that P = 3,500, r = 0.12, m = 12, and n = 6. Solving for Unknowns in the Compound Interest Formula

17. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 17 Example: Upon a child’s birth, a deposit is made into an account. Assume that the account has an annual interest rate of 4.8% and that the compounding is done quarterly. How much must be deposited now so that the child will have $60,000 at age 18? (continued on next slide) Solving for Unknowns in the Compound Interest Formula

18. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 18 Solution: We see that A = 60,000, r = 0.048, m = 72, and n = 4. Solving for Unknowns in the Compound Interest Formula

19. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 19 Example: $1.4 million is to be invested now to be paid as $1.68 million in 2 years. What rate of investment will yield $1.68 million in 2 years? Assume an annual interest rate that is compounded monthly. (continued on next slide) Solving for Unknowns in the Compound Interest Formula

20. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 20 Solution: A =1.68, P =1.4, m =12, and n =24. We wish to solve for r. Solving for Unknowns in the Compound Interest Formula Use the calculator x^(1/y) button to find the 24 th root of 1.2

21. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 21 Loans and loan payments involving compound interest (the most common type of loan) are covered later but, because they involve simple interest, Simple Interest Loans are “simple” enough to tackle with what we already know. Simple Interest Loans Example: Compute the monthly payment for a simple interest loan of $2090 with an annual interest rate of 8% & a 5 year term.

22. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 8.2, Slide 22 Simple Interest Loans Solution: Because simple interest loans have no compounding, to calculate payments, just use the simple interest formula to calculate the future value (A) of the loan and then divide A by the total number of payments due over the term of the loan. Example: Compute the monthly payment for a simple interest loan of $2090 with an annual interest rate of 8% & a 5 year term. A = P(1+rt) = 2090[1+0.08(5)] = 2090(1+0.40) = 2090(1.4) =$2926 If payments are made monthly for 5 years, then there are a total of 12(5) = 60 payments over the term of the loan, so… Monthly payment = $2926 / 60 = $48.77