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Understanding Percentages and Interest Calculations in Financial Scenarios

This guide covers essential calculations involving percentage increases and decreases, as well as interest rate computations for loans and investments. Learn how to determine the effect of a percentage increase on a value, calculate the percent decrease from one number to another, and solve for unknowns such as interest rates and time using the formula (I = P cdot r cdot t). With real-world examples, including loan repayments and investment earnings, this resource will help you grasp the concepts of financial mathematics and improve your problem-solving skills.

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Understanding Percentages and Interest Calculations in Financial Scenarios

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  1. 2 3 16 % Warm Up 1.What is 35 increased by 8%? 2. What is the percent of decrease from 144 to 120? 3. What is 1500 decreased by 75%? 4. What is the percent of increase from 0.32 to 0.64? 37.8 375 100%

  2. Derive formulas for P, r & t I = Pr tMemorize P = I/ (r t)Divide both sides by r*t r = I/(P t)Divide both sides by P*t t = I/(Pr)Divide both sides by P*r

  3. Solving for Interest Rate Mr. Johnson borrowed $8000 for 4 years to make home improvements. If he repaid a total of $10,320, at what interest rate did he borrow the money? P + I = AUse the formula. 8000 + I = 10,320 Substitute. I = 10,320 – 8000 = 2320 Subtract 8000 from both sides. He paid $2320 in interest. Use the amount of interest to find the interest rate.

  4. 1 4 2320 = rDivide both sides by 32,000. 32,000 Mr. Johnson borrowed the money at an annual rate of 7.25%, or 7 %. Example Continued I = Pr tUse the formula. 2320 = 8000 r4 Substitute. 2320 = 32,000 rSimplify. 0.0725 = r

  5. Example: Solving for Time Mr. Mogi borrowed $9000 at an interest rate of 12% to make home improvements. If he repaid a total of $20,000, how long 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 time in years.

  6. 11,000 = tDivide both sides by 1080. 1080 Time Example Continued I = PrtUse the formula. 11,000 = 9000  .12 tSubstitute. 11,000 = 1080 tSimplify. 10.18 = t Mr. Mogi borrowed the money for over 10 years.

  7. Example 2: Solve for Time Nancy invested $6000 in a bond at a yearly rate of 3%. She earned $450 in interest. How long was the money invested? I = P r  t Use the formula. 450 = 6000  0.03 tSubstitute values into the equation. 450 = 180t 2.5 = tSolve for t. The money was invested for 2.5 years, or 2 years and 6 months. Guided Practice 2

  8. Example 3 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. Guided Practice

  9. Homework Instructions Complete ‘I=PxRxT’ Work Sheet Back Side Chart #1-7

  10. Derive formulas for P, r & t I = Pr tMemorize P = I/ (r t)Divide both sides by r*t r = I/(P t)Divide both sides by P*t t = I/(Pr)Divide both sides by P*r

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