Question

How long will it take for a sum of money, invested at 5% compounded annually, to double in value?

Answer 1

Using the compound interest formula, where n=number of years,
2x=x(1+0.05)^n
(1.05)^n=2
=>
n=log(2)/log(1.05)=14.21 years

Note: This problem can also be solved in the head using the rule of 72.
Since the amount is doubled at an interest rate of 5%, the time needed is 72/5=14 years, approximately.