Rule of 72 – Estimation of Compound Interest and Time

Effect of Compounding

The Rule of 72 is a good quick math shortcut to find out the following –

  • Time required for an amount to double itself, at a given rate of interest
  • Rate at which an amount should grow to double itself in given time

This formula can be applied for “Doubling Problems” related to money, population, etc. which grows at an annual compounded rate.

Formulae

  1. To calculate the time; T = 72/R
  2. To calculate the rate of interest; R= 72/T

T = Time required to double a sum of money at the rate of R% per annum.

R = Rate of interest at which a sum of money gets doubled in T years.

Explanation of the formula  

To find out the number of years required to double an investment in a fixed deposit which gives you 9% rate of interest compounding annually, divide 72 by 9.

For example, if you invest Rs. 10000 with compounding interest at a rate of 9% per annum, the rule of 72 gives 72/9 = 8 years required for the investment to become Rs. 20000; an exact calculation gives 8.0432 years. So there is small margin of approximation.

The above formula is more accurate at lower interest rates (say up till 10%). The approximation error starts increasing after that.

In case of continuous compounding, 69 instead of 72, gives more accurate results. However, in our day to day life the concept of continuous compounding is rarely used.

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