College Algebra 5.5 logs

Question

What is the interest rate necessary for an investment to quadruple after 17 years of continuous compound interest?

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula that you want to use here is

A = P*e^(rt)

Then in the scenario we’re solving we have A = 4P since we want the principal amount to quadruple and t = 17

4P = P * e^(17r)

4 = e^(17r)

ln(4) = 17r

r = ln(4) / 17 = 0.0815

meaning that the interest rate needed is approximately 8.15%

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

The formula for continuous compounding is:

 

A = Pe^rt

 

Where:

• A = the final amount = 4P (quadruple the initial investment P)
• P = the principle or initial amount invested
• r = the interest rate
• t = years = 17

 

4P = Pe^17r

4 = e^17r

ln(4) = 17r

ln(4)/17 = r

0.0815 = 8.15% = r