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

Question

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## Answers ( No )

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 yearsNote: 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.