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Understanding Exponential & Logarithmic Equations in Investment Growth

This review focuses on solving exponential and logarithmic equations, particularly in the context of investment and compound interest. It discusses the formulas for future value under different compounding methods, including annual, periodic, and continuous compounding. The examples illustrate how varying rates and compounding frequencies affect investment growth over time, providing insights into strategies for maximizing future value. Key concepts and applications are explored to ensure a comprehensive understanding of how investments can grow through compounding.

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Understanding Exponential & Logarithmic Equations in Investment Growth

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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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