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

Answer: 1 year = $1,127.34,10 Years = $3,315.53, 20 years = $10,992.74, 100 years = $160,520,208.47

Solution and Explanations:

Use the formula

where A is the balance at the end of a certain time period, P is the beginning investment of $1,000, t is the number of years. The annual rate of 12% is converted to a weekly interest rate since the compounding is weekly (52 times per year). Take the annual interest rate of 12% and divide by 52 to obtain the weekly interest rate. The exponent is 52t because there are 52 compounding periods in every year. Therefore, 52t represents the number of compounding periods during t years.

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

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

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

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

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

S.O.S MATHematics home page