6-6 Simple Interest Warm Up Problem of the Day Lesson Presentation Course 2 Warm Up Problem of the Day Lesson Presentation

6-6 Simple Interest Warm Up Multiply. 1. 800  0.04  3 Course 2 6-6 Simple Interest Warm Up Multiply. 1. 800  0.04  3 2. 1,700  2  0.25 3. 900  0.05  4 4. 1,200  6  0.35 96 850 180 2,520

6-6 Simple Interest Problem of the Day 0.75 75% Course 2 6-6 Simple Interest Problem of the Day Which number does not belong in the group? 0.75 75% 3 4 6 8 75 1,000 75 1,000 = ; 3 40 the others equal . 4

6-6 Simple Interest Learn to solve problems involving simple interest. Course 2 6-6 Simple Interest Learn to solve problems involving simple interest.

Insert Lesson Title Here Course 2 6-6 Simple Interest Insert Lesson Title Here Vocabulary interest simple interest principal

Course 2 6-6 Simple Interest When you keep money in a savings account, your money earns interest. Interest is an amount that is collected or paid for the use of money. For example, the bank pays you interest to use your money to conduct its business. Likewise, when you borrow money from the bank, the bank collects interest on its loan to you.

Course 2 6-6 Simple Interest One type of interest, called simple interest, is money paid only on the principal. The principal is the amount of money deposited or borrowed. To solve problems involving simple interest, you can use the following formula. Rate of interest per year (as a decimal) Interest I = P · r · t Time in years that the money earns interest Principal

Additional Example 1A: Using the Simple Interest Formula Course 2 6-6 Simple Interest Additional Example 1A: Using the Simple Interest Formula Find the missing value. A. I = , P = $575, r = 8%, t = 3 years I = P · r · t I = 575 · 0.08 · 3 Substitute. Use 0.08 for 8%. I = $138 Multiply. The simple interest is $138.00.

Additional Example 1B: Using the Simple Interest Formula Course 2 6-6 Simple Interest Additional Example 1B: Using the Simple Interest Formula Find the missing value. B. I = $204, P = $1,700, r = , t = 6 years I = P · r · t 204 = 1,700 · r · 6 Substitute. 204 = 10,200r Multiply. 204 10,200 = 10,200r Divide by 10,200 to isolate the variable. 0.02 = r The interest rate is 2%

6-6 Simple Interest Try This: Example 1A Find the missing value. Course 2 6-6 Simple Interest Try This: Example 1A Find the missing value. A. I = , P = $525, r = 7%, t = 2 years I = P · r · t I = 525 · 0.07 · 2 Substitute. Use 0.07 for 7%. I = $73.50 Multiply. The simple interest is $73.50.

6-6 Simple Interest Try This: Example 1B Find the missing value. Course 2 6-6 Simple Interest Try This: Example 1B Find the missing value. B. I = $600, P = $2,000, r = , t = 3 years I = P · r · t 600 = 2,000 · r · 3 Substitute. 600 = 6,000r Multiply. 600 6000 = 6,000r 6,000 Divide by 10,200 to isolate the variable. 0.1 = r The interest rate is 10%

Understand the Problem Course 2 6-6 Simple Interest Insert Lesson Title Here Additional Example 2: Problem Solving Application Avery deposits $6,000 in an account that earns 4% simple interest. How long will it take for his account balance to reach $6,800? 1 Understand the Problem Rewrite the question as a statement: • Find the number of years it will take for Avery’s account to reach $6,800. List the important information: • The principal is $6,000. • The interest rate is 4%. • His account balance will be $6,800.

Insert Lesson Title Here Course 2 6-6 Simple Interest Insert Lesson Title Here Additional Example 2: Problem Solving Application Avery deposits $6,000 in an account that earns 4% simple interest. How long will it take for his account balance to reach $6,800? 2 Make a Plan Avery’s account balance A includes the principal plus the interest: A = P + I. Once you solve for I, you can use I = P · r · t to find the time.

Additional Example 2: Problem Solving Application Course 2 6-6 Simple Interest Additional Example 2: Problem Solving Application Solve 3 A = P + I Substitute. 6,800 = 6,000 + I –6,000 – 6,000 Subtract to isolate the variable. 800 = I I = P · r · t 800 = 6,000 · 0.04 · t Substitute. Use 0.04 for 4%. 800 = 240t Multiply. 800 240 = 240t Divide to isolate the variable. 3.33  t Round to the nearest hundredth. 1 3 It will take 3 years.

Additional Example 2: Problem Solving Application Course 2 6-6 Simple Interest Additional Example 2: Problem Solving Application 4 Look Back 1 3 After exactly 3 years, Avery’s money will have earned $800 in simple interest and his account balance will be $6,800. 1 3 I = 6,000 · 0.04 · 3 = 800 1 3 So it will take 3 years to reach $6,800.

Understand the Problem Course 2 6-6 Simple Interest Insert Lesson Title Here Try This: Example 2 Linda deposits $10,000 in an account that earns 8% simple interest. How long will it take for the total amount in her account to reach $12,000? 1 Understand the Problem Rewrite the question as a statement: • Find the number of years it will take for Linda’s account to reach $12,000. List the important information: • The principal is $10,000. • The interest rate is 8%. • Her account balance will be $12,000.

Insert Lesson Title Here Course 2 6-6 Simple Interest Insert Lesson Title Here Try This: Example 2 Linda deposits $10,000 in an account that earns 8% simple interest. How long will it take for the total amount in her account to reach $12,000? 2 Make a Plan Linda’s account balance A includes the principal plus the interest: A = P + I. Once you solve for I, you can use I = P · r · t to find the time.

6-6 Simple Interest Try This: Example 2 Solve 3 A = P + I Substitute. Course 2 6-6 Simple Interest Try This: Example 2 Solve 3 A = P + I Substitute. 12,000 = 10,000 + I –10,000 –10,000 Subtract to isolate the variable. 2,000 = I I = P · r · t 2,000 = 10,000 · 0.08 · t Substitute. Use 0.08 for 8%. 2,000 = 800t Multiply. 2,000 800 = 800t Divide to isolate the variable. 2.5 = t 1 2 It will take 2 years.

6-6 Simple Interest Try This: Example 2 4 Look Back Course 2 6-6 Simple Interest Try This: Example 2 4 Look Back 1 2 After exactly 2 years, Linda’s money will have earned $2,000 in simple interest and her account balance will be $12,000. 1 2 I = 10,000 · 0.08 · 2 = 12,000 1 2 So it will take 2 years to reach $12,000.

Insert Lesson Title Here Course 2 6-6 Simple Interest Insert Lesson Title Here Lesson Quiz Find each missing value. 1. I = 2. I = $18, P = $150, r = 3. I = $640, P = 4. I = $120, P = $600, r = 5% t = , P = $800, r = 10%, t = 3 years $240 , t = 2 years 6% , r = 4%, t = 8 years $2,000 4 years 5. Dennis deposits $6,000 in an account that earns 5.5% simple interest. How long will it take before the total amount is $8,000? a little over 6 years