APPLICATIONS OF EXPONENTIAL AND
LOGARITHMIC FUNCTIONS

(Interest Rate Word Problems)

1. To solve an exponential or logarithmic word problems, convert the narrative to an equation and solve the equation.

Problem 5: If you invested $1,000 in an account paying an annual percentage rate (quoted rate) of 12%, compounded continuously, how much would you have in you account at the end of 1 year, 10 years, 20 years, 100 years?

Answer: 1 Year = $1,127.50, 10 years = $3,320.12, 20 years = $11,023.18, 100 years $162,754,791.42

Solution and Explanations:
Use the formula

displaymath31

where A is the balance at the end of a certain time period, P is the beginning investment of $1,000, the annual interest rate is 12%, and t is the number of years.

To find the balance at the end of 1 year:
Substitute 1 for t in the equation tex2html_wrap_inline33 to derive A:

displaymath35

To find the balance at the end of 10 year:
Substitute 10 for t in the equation tex2html_wrap_inline33 to derive A:

displaymath39

To find the balance at the end of 20 year:
Substitute 20 for t in the equation tex2html_wrap_inline33 to derive A:

displaymath43

To find the balance at the end of 100 year:
Substitute 100 for t in the equation tex2html_wrap_inline33 to derive A:

displaymath47

If you would like to work another problem and check the answer and solution, click on Problem.

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Author: Nancy Marcus

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