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

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.