MAT 150 - Class #19
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MAT 150 - Class #19
Review Solving Exponential and Logarithmic Equations
Exponential Functions & Investing
Solve the Logarithmic
Equations
A Better Understandin
g of How Compound
Interest Works
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
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
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
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
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?
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
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
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!!!!
Pg. 378-380#3-7 odd#17-27 odd#42-43#46-47
Assignment
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