Question

Ethan has $240,000 to invest today at an annual interest rate of 4%. Approximately how many years will it take before the investment grows to $486,000?

Answer 1

17.98972134

18 years

Step-by-step explanation:

Using the compound interest formula we can solve for time

`Principal * (1+ r)^(time) = Amount`

We post our know values

`240,000* (1+ 0.04)^(time) = 486,000`

And solve for the unknow

`(1.04)^(time) =486,000/240,000\\(1.04)^(time) = 2.025`

Now we have to use log properties to solve for time

`log_(1.04)2.025 = time`

`(\log 2.025)/(\log 1.04) =17.98972134`

It will take 18 years