Question

Suppose $2,400 is invested in an account at an annual interest rate of 6.1% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size?

Answer 1

You want to find the number of years, call it 'T' (time) such that after T years, you have $4,800.

After 1 year, you will have $2,400*1.061.
So you want to solve the equation $2,400*(1.061)^T = $4,800.

That is, 1.061^T = 2.

So taking logs of both sides, with base 1.061, you get T = log(base 1.061) of 2.
Put that into a calculator to get the answer :)