Simple and Compound Interest PREALGEBRA LESSON 7 8

Simple and Compound Interest PRE-ALGEBRA LESSON 7 -8 Use your classmates as subjects and estimate these percents. a. About what percent are girls? b. About what percent are twins? Check students’ answers. 7 -8

Simple and Compound Interest PRE-ALGEBRA LESSON 7 -8 (For help, go to Lesson 6 -6. ) Find each amount. 1. 6% of $400 2. 55% of $2, 000 3. 4. 5% of $700 4. 5 2 % of $325 1 Check Skills You’ll Need 7 -8

Simple and Compound Interest PRE-ALGEBRA LESSON 7 -8 Solutions 1. 6 x = 100 400 2. 6(400) = 100 x 55(2000) = 100 x 6(400) x = 100 55(2000) 100 x = 100 $24 = x 3. 55 x = 100 2000 4. 5 x = 100 700 $1, 100 = x 4. 5. 5 x = 100 325 4. 5(700) = 100 x 5. 5(325) = 100 x 4. 5(700) 100 x = 100 5. 5(325) 100 x = 100 $31. 50 = x $17. 88 = x 7 -8

Simple and Compound Interest PRE-ALGEBRA LESSON 7 -8 Suppose you deposit $1, 000 in a savings account that earns 6% per year. a. Find the interest earned in two years. Find the total of principal plus interest. I = prt Use the simple interest formula. I = 1, 000 • 0. 06 • 2 Replace p with 1, 000, r with 0. 06, and t with 2. I = 120 Simplify. total = 1, 000 + 120 = 1, 120 Find the total. The account will earn $120 in two years. The total of principal plus interest will be $1, 120. 7 -8

Simple and Compound Interest PRE-ALGEBRA LESSON 7 -8 (continued) b. Find the interest earned in six months. Find the total of principal plus interest. 6 1 t = 12 = = 0. 5 2 Write the months as part of a year. I = prt Use the simple interest formula. I = 1, 000 • 0. 06 • 0. 5 Replace p with 1, 000, r with 0. 06, and t with 0. 5. I = 30 Simplify. Total = 1, 000 + 30 = 1, 030 Find the total. The account will earn $30 in six months. The total of principal plus Quick Check interest will be $1, 030. 7 -8

Simple and Compound Interest PRE-ALGEBRA LESSON 7 -8 Quick Check You deposit $400 in an account that earns 5% interest compounded annually (once per year). The balance after the first four years is $486. 20. What is the balance in your account after another 4 years, a total of 8 years? Round to the nearest cent. Principal at Beginning of Year Interest Balance Year 5 : $486. 20 • 0. 05 = 24. 31 486. 20 + 24. 31 = 510. 51 Year 6 : $510. 51 • 0. 05 25. 53 510. 51 + 25. 53 = 536. 04 Year 7 : $536. 04 • 0. 05 26. 80 536. 04 + 26. 80 = 562. 84 Year 8 : $562. 84 • 0. 05 28. 14 562. 84 + 28. 14 = 590. 98 After the next four years, for a total of 8 years, the balance is $590. 98. 7 -8

Simple and Compound Interest PRE-ALGEBRA LESSON 7 -8 Find the balance on a deposit of $2, 500 that earns 3% interest compounded semiannually for 4 years. The interest rate r for compounding semiannually is 0. 03 ÷ 2, or 0. 015. The number of payment periods n is 4 years 2 interest periods per year, or 8. B = p(1 + r)n Use the compound interest formula. B = 2, 500(1 + 0. 015)8 Replace p with 2, 500, r with 0. 015, and n with 8. B Use a calculator. Round to the nearest cent. 2, 816. 23 The balance is $2, 816. 23. Quick Check 7 -8

Simple and Compound Interest PRE-ALGEBRA LESSON 7 -8 Find the simple interest and the balance. 1. $1, 200 at 5. 5% for 2 years 2. $2, 500 at 8% for 6 months $132; $1, 332 $100; $2, 600 3. Find the balance on a deposit of $1, 200, earning 9. 5% interest compounded semiannually for 10 years. $3, 035. 72 7 -8