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

Answer: 1 year = $1,125.51,10 Years = $3,262.04, 20 years = $10,640.89, 100 years = $136,423,718.23

Solution and Explanations:

Use the formula

displaymath41

where A is the balance at the end of a certain time period, P is the beginning investment, t is the number of years. The annual rate of 12% is converted to a quarterly interest rate since the compounding is quarterly (4 times per year). Take the annual interest rate of 12% and divide by 4 to obtain the quarterly interest rate. The exponent is 4t because there are 4 compounding periods in every year. Therefore, 4t represents the number of compounding periods during t years.

To find the balance at the end of 1 year:
Substitute $1,000 for P and 1 for t in the equation tex2html_wrap_inline43 to derive A:

displaymath45

To find the balance at the end of 10 year:
Substitute $1,000 for P and 10 for t in the equation tex2html_wrap_inline43 to derive A:

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To find the balance at the end of 20 year:
Substitute $1,000 for P and 20 for t in the equation tex2html_wrap_inline43 to derive A:

displaymath53

To find the balance at the end of 100 year:
Substitute $1,000 for P and 100 for t in the equation tex2html_wrap_inline43 to derive A:

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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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