(Interest Rate Word Problems)
1. To solve an exponential or logarithmic word problems, convert the narrative to an equation and solve the equation.
Problem 4: If you invested $1,000 in an account paying an annual
percentage rate (quoted rate) of 12%, compounded hourly (based
on a bank year of 360 days), 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 = $3,320.09, 20 years =
$11,022.99, 100 years $162,741,385.44
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, and t is the number of years. The annual rate of 12% is converted to a hourly interest rate (based on a bank year of 360 days) since the compounding is hourly (24 x 360 times per year). Take the annual interest rate of 12% and divide by 8640 to obtain the hourly interest rate. The exponent is 8640t because there are 8,640 compounding periods in every year. Therefore, 8640t represents the number of compounding periods during t years.
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Author: Nancy Marcus