College Algebra Word Problem

Question

A $2500 investment is made at a 5% annual interest rate compounded continuously. Use the compound interest formula for continuous compounded interest to determine how long it would take for the balance in the account to reach $5000. Round your answer to the nearest tenth of a year.

 

It will take __________ years.

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) for continuous compounding

Then in the scenario we’re solving

5000 = 2500e^(0.05t)  since the interest rate is 5% and we’re trying to go from 2500 to 5000

Solving that for the value of t yields

2 = e^(0.05t)

ln(2) = 0.05t

t = ln(2) / 0.05 = 13.8629

meaning that it will take about 13.9 years for the balance to reach $5000

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

Continuous compounding formula:

A(t) = A₀e^rt 

 

A₀ = 2500

r = 0.05

 

A(t) = 2500e^0.05t = 5000

Simplify

e^0.05t = 2

Take the natural logarithm of each side.

0.05t = ln(2)

t = 0.6931 / 0.05

t = 13.9 years