Suppose 3000 is invested in an account at an annual interest

Suppose $3,000 is invested in an account at an annual interest rate of 4.6% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size?

Solution

The formula for interest that is compounded is

A=P(1+r/n)^nt

6000 = 3000 * (1 + 0.046)^t

2 = (1.046)^t

ln(2) = t ln(1.046)

t = ln(2) / ln(1.046)

= 0.30103 / 0.01953

= 15.41

t = 15.41 i.e 15 years