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MAT 150 - Class #19

MAT 150 - Class #19. Review Solving Exponential and Logarithmic Equations Exponential Functions & Investing. Solve the Logarithmic Equations. A Better Understanding of How Compound Interest Works. Equations for Future Value of an Investment. Annual Compounding P = invested

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MAT 150 - Class #19

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  1. MAT 150 - Class #19 Review Solving Exponential and Logarithmic Equations Exponential Functions & Investing

  2. Solve the Logarithmic Equations

  3. A Better Understanding of How Compound Interest Works

  4. Equations for Future Value of an Investment Annual Compounding P = invested r = rate (always a decimal) t = years S = future value Periodic Compounding P = invested r = rate (always a decimal) k = compounded times per year t = years S = future value

  5. P = invested r = rate (always a decimal) t = years S = future value Annual Compounding Suppose $6400 is invested for x years at 7% interest, compounded annually. • Find the future value of this investment at the end of 10 years. • In how many years will it take to reach $48,718?

  6. Periodic Compounding Interest

  7. Periodic Compounding Interest • If $8800 is invested at 6% interest, compounded semiannually, find the future value in 10 years. • Would you have more money if compounded daily and if so, how much? P = invested r = rate (always a decimal) k = compounded times per year t = years S = future value

  8. What do you think happens to the investment as the number of Periods per year increases? • Consider $1 invested at an annual rate of 100% compounded for 1 year with different compounding periods. Find the future values. • Was your theory correct? • Could you change anything to make the future values increase quicker?

  9. Compounding Continuously • This formula allows the interest to compound ALL THE TIME. • Look back at example 3. Do you notice what the numbers in the table are approaching?

  10. Continuous Compounding • What is the future value of $2650 invested for 8 years at 12% compounded continuously? • Compare this to an interest compounded annually. Which type of compounding created a larger future value and by how much?

  11. 1 MILLION DOLLARS!!!! Mr. Kolstonwants to be a millionaire by the time he is 55 years of age but doesn’t want to work to do it. He has found a fund that has an interest rate of 13% and is compounded monthly. How much would he have to put in now in order to make his dreams come true?

  12. Assignment Pg. 378-380 #3-7 odd #17-27 odd #42-43 #46-47

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