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Lesson 7.8: Simple Interest

Lesson 7.8: Simple Interest. If someone borrows money, what factors influence how much is paid back?. Principal -. How much was borrowed. Time -. How long it was borrowed for. (in years). Rate -. What interest was charged. (annual % rate). Amount to Payback =. Principal. +.

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Lesson 7.8: Simple Interest

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  1. Lesson 7.8: Simple Interest

  2. If someone borrows money, what factors influence how much is paid back? Principal - How much was borrowed. Time - How long it was borrowed for. (in years) Rate - What interest was charged. (annual % rate) Amount to Payback = Principal + Interest Interest = Principal Rate Time

  3. Joe borrows $200 from the bank at 6% simple interest for 3 years. What interest does he owe, and what is his total balance (amount to payback)? Interest Balance Balance = P + I Balance = 200 + 36 Balance = 236 Balance = $236

  4. Juan invests $5000 in bonds for 6 months at an annual interest rate of 7%. How much interest did he earn, and what is the balance in his account? Interest Balance Balance = P + I Balance = 5000 + 175 Balance = 5175 Balance = $5175

  5. Find the simple interest and the balance. Balance = P + I Balance = 2000 + 60 Balance = $2060

  6. Find the annual simple interest rate.

  7. Find the annual simple interest rate.

  8. Find the principal amount invested.

  9. Quick Draw for Points • You will have 60 seconds to solve each problem • The text is Simple Interest Problems

  10. Example 1: Finding Interest on a Loan To buy a car, Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay if she pays the entire loan off at the end of the third year? First, find the interest she will pay. I = PrtUse the formula. I = 15,000  0.09 3 Substitute. Use 0.09 for 9%. • I = 4050Solve for I.

  11. Example 1A: Finding Total Payment on a Loan What is the total amount that she will repay? Jessica will pay $4050 in interest. You can find the total amount A to be repaid on a loan by adding the principal P to the interest I. P+ I = Aprincipal + interest = total amount 15,000 + 4050 = ASubstitute. • 19,050 = ASolve for A. Jessica will repay a total of $19,050 on her loan.

  12. Example 2 TJ invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested? I = PrtUse the formula. 200 = 4000  0.02 t Substitute values into the equation. 200 = 80t • 2.5 = tSolve for t. The money was invested for 2.5 years, or 2 years and 6 months.

  13. Example 3 Bertha deposited $1000 into a retirement account when she was 18. How much will Bertha have in this account after 50 years at a yearly simple interest rate of 7.5%? I = PrtUse the formula. I = 1000  0.075  50 Substitute. Use 0.075 for 7.5%. • I = 3750 Solve for I. The interest is $3750. Now you can find the total.

  14. Example 3 Continued P + I = AUse the formula. 1000 + 3750 = A Substitute. • 4750 = ASolve for A. Bertha will have $4750 in the account after 50 years.

  15. Example 4 Mr. Mogi borrowed $9000 for 10 years to make home improvements. If he repaid a total of $20,000 at what interest rate did he borrow the money? P + I = AUse the formula. 9000 + I = 20,000 Substitute. I = 20,000 – 9000 = 11,000 Subtract 9000 from both sides. He paid $11,000 in interest. Use the amount of interest to find the interest rate.

  16. 11,000 = rDivide both sides by 90,000. 90,000 0.12 = r Example 4 Continued I = PrtUse the formula. 11,000 = 9000 r10 Substitute. 11,000 = 90,000 rSimplify. Mr. Mogi borrowed the money at an annual rate of about 12.2%.

  17. Summary • I = __________ • P=__________ • r = __________ • t = __________ • A=__________ • Interest Formula: I = ( )( )( ) • Amount Formula: A = ___ + ___

  18. SUMMARY Principal - How much was __________. Time - How _____it was borrowed for. (in_____) Rate - What _______was charged. (annual % rate) Amount to Payback = Principal + Interest Interest = ________ ____ ______

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