Holt CA Course Simple Interest Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

Holt CA Course Simple Interest Warm Up Multiply  0.04  ,700  2   0.05  ,200  6  ,520

Holt CA Course Simple Interest NS1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. Also covered: AF1.1 California Standards

Holt CA Course Simple Interest Vocabulary interest simple interest principal

Holt CA Course 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.

Holt CA Course 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. I = P · r · t Simple interest is money paid only on the principal Principal is the amount borrowed or invested Rate of interest is the percent charged or earned Time that the money is borrowed or invested (in years) Notice that the interest rate is expressed as a decimal and the time is expressed in years.

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

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

Holt CA Course Simple Interest 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.

Holt CA Course Simple Interest 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 Continued

Holt CA Course Simple Interest Solve. 3 A = P + I 6,800 = 6,000 + I 800 = I I = P · r · t 800 = 6,000 · 0.04 · t 800 = 240t 3.33  t It will take years. Substitute. Subtract from each side. Substitute. Use 0.04 for 4%. Multiply. Divide each side by 240. Round to the nearest hundredth. –6,000 – 6, = 240t 240 Additional Example 2 Continued

Holt CA Course Simple Interest Look Back 4 After exactly 3 years, Avery’s money will have earned $800 in simple interest and his account balance will be $6, I = 6,000 · 0.04 · = 800 An answer of 3 years for the account to reach $6,800 makes sense Additional Example 2 Continued

Holt CA Course Simple Interest Find the missing value. Check It Out! Example 1 A. I = $600, P = $2,000, r =, t = 3 years I = P · r · t 600 = 2,000 · r · = 6,000r = 6,000r 6, = r The interest rate is 10%. Substitute. Multiply. Divide each side by 6,000.

Holt CA Course Simple Interest Check It Out! 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.

Holt CA Course Simple Interest 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. Check It Out! Example 2 Continued

Holt CA Course Simple Interest Solve 3 A = P + I 12,000 = 10,000 + I 2,000 = I I = P · r · t 2,000 = 10,000 · 0.08 · t 2,000 = 800t 2.5 = t It will take years. Substitute. Subtract 10,000 from each side. Substitute. Use 0.08 for 8%. Multiply. Divide each side by 800. –10,000 2, = 800t 800 Check It Out! Example 2 Continued

Holt CA Course Simple Interest Look Back 4 After exactly 2 years, Linda’s money will have earned $2,000 in simple interest and her account balance will be $12, I = 10,000 · 0.08 · = 12,000 An answer of 2 years for the account to reach $12,000 makes sense Check It Out! Example 2 Continued

Holt CA Course Simple Interest 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 = 6% $240 $2,000 4 years, P = $800, r = 10%, t = 3 years, t = 2 years, r = 4%, t = 8 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