1. © 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 8 Consumer Mathematics and Financial Management

2. © 2010 Pearson Prentice Hall. All rights reserved. 2 8.2 Simple Interest

3. © 2010 Pearson Prentice Hall. All rights reserved. 3 Objectives 1.Calculate simple interest. 2.Use the future value formula. 3.Use the simple interest formula on discounted loans.

4. © 2010 Pearson Prentice Hall. All rights reserved. 4 Simple Interest Interest is the dollar amount that we get paid for lending money or pay for borrowing money. The amount of money that we deposit or borrow is called the principal. The amount of interest depends on the principal, the interest rate, which is given as a percent and varies from bank to bank, and the length of time for which the money is deposited. Simple interest involves interest calculated only on the principal.

5. © 2010 Pearson Prentice Hall. All rights reserved. 5 Simple Interest To calculate simple interest: Interest = principal  rate  time I = Prt The rate r, is expressed as a decimal when calculating simple interest.

6. © 2010 Pearson Prentice Hall. All rights reserved. 6 You deposit $2000 in a savings account at Hometown Bank, which has a rate of 6%. Find the interest at the end of the first year. Solution: To find the interest at the end of the first year, we use the simple interest formula. At the end of the first year, the interest is $120. Example 1: Calculating Simple Interest for a Year

7. © 2010 Pearson Prentice Hall. All rights reserved. A student took out a simple interest loan for $1800 for two years at a rate of 8% to purchase a used car. Find the interest on the loan. Solution: To find the interest of the loan, we use the simple interest formula. The interest on the loan is $288. 7 Example 2: Calculating Simple Interest for More Than a Year

8. © 2010 Pearson Prentice Hall. All rights reserved. 8 Future Value: Principal Plus Interest The future value, A, of P dollars at simple interest rate r (as a decimal) for t years is given by A = P(1 + rt). P is also known as the loan’s present value.

9. © 2010 Pearson Prentice Hall. All rights reserved. 9 Example 3: Calculating Future Value A loan of $1060 has been made at 6.5% for three months. Find the loan’s future value. Solution: The variables are given as follows: P = $1060 r = 6.5% or 0.065 t = ¼ = 0.25 since 3 months is 1/4 of a year. Use the future value formula: A = P(1 + rt) A = 1060(1 + 0.065 · 0.25) A ≈ $1077.23 Rounded to the nearest cent, the loan’s future value is $1077.23.

10. © 2010 Pearson Prentice Hall. All rights reserved. 10 You borrow $2500 from a friend and promise to pay back $2655 in six months. What simple interest will you pay? Solution: Substitute A = $2655 P = $2500 t = ½ or 0.5 Example 4: Determining a Simple Interest Rate

11. © 2010 Pearson Prentice Hall. All rights reserved. 11 You will pay a simple interest rate of 12.4%. Example 4: Determining a Simple Interest Rate continued

12. © 2010 Pearson Prentice Hall. All rights reserved. 12 Discounted Loans Some lenders collect the interest from the amount of the loan at the time that the loan is made. This is called a discounted loan. The interest that is deducted from the loan is the discount.

13. © 2010 Pearson Prentice Hall. All rights reserved. 13 Example 6: Discounted Loan You borrow $10,000 on a 10% discounted loan for a period of 8 months. a.What is the loan’s discount? b.Determine the net amount of money you receive. c.What is the loan’s actual interest rate? Solution: a.Because the loan’s discount is the deducted interest, we use the simple interest formula.

14. © 2010 Pearson Prentice Hall. All rights reserved. 14 b.The net amount that you receive is the amount of the loan, $10,000, minus the discount, $666.67: 10,000 – 666.67 = 9333.33. Thus, you receive $9333.33. c.We can recalculate the loan’s actual interest rate, rather than stated 10%, by using the simple interest formula. Example 6: Discounted Loan continued The actual rate of interest on the 10% discounted loan is approximately 10.7%.