MAT 150 - Class #19
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Transcript of MAT 150 - Class #19
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MAT 150 - Class #19
Review Solving Exponential and Logarithmic Equations
Exponential Functions & Investing
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Solve the Logarithmic
Equations
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A Better Understandin
g of How Compound
Interest Works
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Annual Compounding
P = investedr = rate (always a decimal) t = yearsS = future value
Periodic Compounding
P = investedr = rate (always a decimal) k = compounded times per yeart = years S = future value
Equations for Future Value of an Investment
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Suppose $6400 is invested for x years at 7% interest, compounded annually.
A. Find the future value of this investment at the end of 10 years.
B. In how many years will it take to reach $48,718?
Annual Compounding
P = investedr = rate (always a decimal) t = yearsS = future value
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Type of Compounding Number of Periods per Year
( k = ….)Annually 1
Semi-Annually 2Quarterly 4Monthly 12
Daily 365Hourly 8760
Each Minute 525,600
Periodic Compounding
Interest
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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?
Periodic Compounding
Interest
P = investedr = rate (always a decimal) k = compounded times per yeart = years S = future value
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Consider $1 invested at an
annual rate of 100% compounded for 1 year with different compounding periods. Find the future values.
Was your theory correct?
Could you change anything to make the future values increase quicker?
Type of Compounding
Future Value$
Annually
Semi-Annually
Quarterly
Monthly
Daily
Hourly
Each Minute
What do you think happens to the investment as the number of Periods per year increases?
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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?
Compounding Continuously
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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?
Continuous Compounding
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Mr. Kolston wants 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?
1 MILLION DOLLARS!!!!
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Pg. 378-380#3-7 odd#17-27 odd#42-43#46-47
Assignment