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

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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 - PowerPoint PPT Presentation

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Page 1: MAT 150 - Class #19

MAT 150 - Class #19

Review Solving Exponential and Logarithmic Equations

Exponential Functions & Investing

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=jjbJLW6ZinOi8M&tbnid=IsM6ipgorKYtxM:&ved=0CAUQjRw&url=https://xkcd.com/947/&ei=GzvSUeG8E7TUyQGhxoCQAw&bvm=bv.48572450,d.aWc&psig=AFQjCNHCwVOTGg-nQMgjiPJ3cRUsxS6wjw&ust=1372818449726706
Page 2: MAT 150 - Class #19

Solve the Logarithmic

Equations

Page 3: MAT 150 - Class #19

A Better Understandin

g of How Compound

Interest Works

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=4aHvZb63ZsXXtM&tbnid=9QyCEOMrTZ_YqM:&ved=0CAUQjRw&url=http://www.cartoonstock.com/directory/c/compound_interest.asp&ei=UzvSUYa4OeqRyAHI8oCwDg&bvm=bv.48572450,d.aWc&psig=AFQjCNHCwVOTGg-nQMgjiPJ3cRUsxS6wjw&ust=1372818449726706
Page 4: MAT 150 - Class #19

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

Page 5: MAT 150 - Class #19

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

Page 6: MAT 150 - Class #19

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

Page 7: MAT 150 - Class #19

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

http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=AR3qzDhbdL2mNM&tbnid=8kRIkifjsVYtYM:&ved=&url=http://en.wikipedia.org/wiki/File:Stacks_of_money.jpg&ei=U0TSUcu-MaHBywHy9IHoDQ&psig=AFQjCNFVjyQyCFBLOAElqO5HUCwa5MjWhQ&ust=1372820947856072
Page 8: MAT 150 - Class #19

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?

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=zUIkeHJbMuCogM&tbnid=dvQPrDhvC7NLhM:&ved=0CAUQjRw&url=http://www.businessinsider.com/11-personal-finance-equations-you-need-to-know-2012-7?op=1&ei=9kHSUcCvH6KQyAHB3YCgDQ&bvm=bv.48572450,d.aWc&psig=AFQjCNFMMYsGCPfa7MAvcEsCQZz-NQkH6g&ust=1372820327256454
Page 9: MAT 150 - Class #19

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

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=-UyPF1qLLLkBaM&tbnid=jPHsL1kYGzYj8M:&ved=0CAUQjRw&url=http://www.coolmath.com/algebra/17-exponentials-logarithms/04-continuous-compound-interest-02.htm&ei=EEfSUZ6tIcibygG91YHwBQ&bvm=bv.48572450,d.aWc&psig=AFQjCNEYx8lSk9bo7GZLb50NqJDrPYFsog&ust=1372821624490782
Page 10: MAT 150 - Class #19

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

Page 11: MAT 150 - Class #19

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!!!!

Page 12: MAT 150 - Class #19

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

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