# You go to the bank and deposit $2,500 into your savings. Your bank has annual interest rate of 8%, compounded monthly. How long would it take the investment to reach $5,000?

##### 1 Answer

It would take 8 years and nine months for the investment to surpass $5,000.

#### Explanation:

The general formula for compound interest is

Where

Before we start plugging numbers into our equation, let's solve the equation for

Divide both sides by

Take the natural log of both sides. Why the NATURAL log? Because it's the natural thing to do. Sorry, a little math humor there. In reality it really doesn't matter what base you use as long as you apply the same base to both sides of the equation. Try it with

Divide both sides by

NOW we start plugging in numbers!

8.693 years is 8 years and