Simple and Compound Interest

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

1 2 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 % of $325 Check Skills You’ll Need 7-8

x 2000 = 55(2000) 100 100x 100 6(400) 100 = = 5.5(325) 100 4.5(700) 100 100x 100 100x 100 = = x 700 55 100 6 100 x 400 5.5 100 4.5 100 x 100 x 325 = = = Simple and Compound Interest PRE-ALGEBRA LESSON 7-8 1.2. 6(400) = 100x 55(2000) = 100x $24 = x $1,100 = x 3.4. 4.5(700) = 100x 5.5(325) = 100x $31.50 = x $17.88 = x Solutions 7-8

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. 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. The account will earn $120 in two years. The total of principal plus interest will be $1,120. 7-8

1 2 t = = = 0.5 Write the months as part of a year. 6 12 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. 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. The account will earn $30 in six months. The total of principal plus interest will be $1,030. Quick Check 7-8

Year 6 : $510.51 510.51 • 0.05 25.53 510.51 + 25.53 = 536.04 Year 7 : $536.04 536.04 • 0.05 26.80 536.04 + 26.80 = 562.84 Year 8 : $562.84 562.84 • 0.05 28.14 562.84 + 28.14 = 590.98 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 : $486.20 486.20 • 0.05 = 24.31 486.20 + 24.31 = 510.51 After the next four years, for a total of 8 years, the balance is $590.98. 7-8

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. Use a calculator. Round to the nearest cent. B 2,816.23 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. 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 3. Find the balance on a deposit of $1,200, earning 9.5% interest compounded semiannually for 10 years. $132; $1,332 $100; $2,600 $3,035.72 7-8

Simple and Compound Interest