Barry knows that the interest rate is critical to the speed at which your invest

Question

Barry knows that the interest rate is critical to the speed at which your investment grows. For instance, if $1 is invested at 2% compounded annually, it takes approximately 34.9 years to double. If $1 is invested at 5% compounded annually, it takes approximately to double. If $1 is invested at 5% compounded annually, it takes approximately 14.2 years to double. Determine how many years it takes $1 to double if invested at 10% compounded annually; at 12% compounded annually.

Hint: The easiest way to get the answer is to use the Rule of 72.

Please provide step by step explanation.

Explanation / Answer

Solution:

A=P(1+i/n)nt -> 2 = 1 (1+0.1/1)1*t

   -> 2 = (1.1)t

-> log10 2 = t* log10(1.1)

-> t = log10 2 / log10(1.1) = 7.3 years

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