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# CM30S - 1.22

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### CM30S - 1.22

1. 1. Consumer Math 30S Unit 1 – Income & Debt Compound Interest
2. 2. Compound Interest An investment earns compound interest when the interest from each time period is added to the principal and earns interest in subsequent time periods. Because the principal grows, the interest earned grows as well. Compounding makes a significant difference in the final amount an investment is worth. Although compounding interest earns you more money when you are investing, compounding interest costs you more when you borrow. Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems
3. 3. Compound Interest Unit 1 – Income & Debt Outcome 1-1: Solve problems involving performance based income
4. 4. <ul><li>Compound Interest </li></ul><ul><li>What is compound interest? </li></ul><ul><li>Interest which is calculated not only on the initial principal but also the accumulated interest of prior periods. </li></ul><ul><li>A = P(1 + ) </li></ul>r n nt Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems
5. 5. Compound Interest A = P(1 + ) A total amount, including principal and interest P the amount of principal, loan, or deposit r rate expressed as a decimal n the number of compounding periods per year t time in years   What affect will there be on the total amount (A) if . . .   . . . the amount of time is increased?   . . . the number of compounding periods doubled? r n nt Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems
6. 6. Example Problem: Monica wants to invest \$1000 at 7½% for 3 years compounded quarterly. What will be the total value of her investment at the end. Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems
7. 7. <ul><li>Rule of 72 </li></ul><ul><li>The rule of 72 states that to find the approximate time that an amount of money will take to double, divide 72 by the rate (r). To find the rate needed for money to double in a specific time frame, you divide 72 by the number of years. </li></ul><ul><li>For example, \$100 invested at 6% compounded annually would double to \$200 in approximately 12 years </li></ul><ul><li>(72 ÷ 6 = 12). </li></ul>Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems
8. 8. Example Problem: How long does it take for an investment to double if the rate is 12%? Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems
9. 9. Compound Interest Activity Step 1 Each student roles a die 4 times and records the numbers rolled. Step 2 Repeat Step 1 three more times to have a total of 4 trials. Step 3 Determine the compound interest formula for each trial as outlined below. Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems
10. 10. Compound Interest Activity - continued Step 4 Write down your 4 formulas on the board. Step 5 Look at all formulas and predict which one will result in the most amount of money (A). Step 6 Determine the total amount A for your own 4 formulas. Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems
11. 11. Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems
12. 12. Textbook Assignment: Page 38 - 39 Questions 1 - 10 Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems
13. 13. Compound Interest Review Worksheet Questions 1 - 9 Unit 1 – Income & Debt Outcome 1-2: Use simple and compound interest calculations to solve problems