Rule of 72

Rule of 72 

A useful rule of thumb for the time it takes an investment to

double with discrete compounding is the ‘Rule of 72’. To use the Rule of 72,

you simply divide 72 by the interest rate to determine the number of periods it

takes for a value today to double. For example, if the interest rate is 6 per cent,

the Rule of 72 says it will take 72/6 = 12 years to double. This is approximately

equal to the actual answer of 11.90 years. The Rule of 72 can also be applied to

determine what interest rate is needed to double money in a specified period.

This is a useful approximation for many interest rates and periods. At what rate

is the Rule of 72 exact? A corollary to the Rule of 72 is the Rule of 69.3. The

Rule of 69.3 is exactly correct except for rounding when interest rates are

compounded continuously. Prove the Rule of 69.3 for continuously

compounded interest.