Rule of 72: Estimation of Compound Interest and Time

Effect of Compounding

The Rule of 72 is a good quick math shortcut to estimate the effect of any growth rate, from quick financial calculations to population estimates for finding out:

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

Formula

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.

 
This formula is useful for financial estimates for understanding the nature of compound interest and can be applied for “Doubling Problems” related to money, population, etc. which grows at an annual compounded rate.

Explanation of the formula

The Rule of 72 states that, roughly speaking; money will double in 72 r years when it is invested at an annual compounded interest rate of r%.

So, for example, if we invest money at an 8% compounded annual interest rate, it will double its value in 72/8 = 9 years. Similarly, if we leave our money in the bank at a compounded rate of 6%, it would take 12 years for this sum to double its value.

For example, if you invest $10,000 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 $20,000; 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.

For tripling money we would have a “Rule of 114.”

• If your country’s GDP grows at 3% a year, the economy doubles in 72/3 or 24 years.
• If your growth slips to 2%, it will double in 36 years. If growth increases to 4%, the economy doubles in 18 years. Given the speed at which technology develops, shaving years off your growth time could be very important.

You can also use the rule of 72 for expenses like inflation or interest:

• If inflation rates go from 2% to 3%, your money will lose half its value in 36 or 24 years.
• If college tuition increases at 5% per year (which is faster than inflation), tuition costs will double in 72/5 or about 14.4 years. If you pay 15% interest on your credit cards, the amount you owe will double in only 72/15 or 4.8 years!

At a glance

• Have an investment growing at 10% interest? It will double in 7.2 years.
• Want your investment to double in 5 years? You need 72/5 or about 15% interest.
• Growing at 2% a week? You’ll double in 72/2 or 36 weeks. You can use this rule for any duration of time, not just years.
• Inflation at 4%? It will halve your money in 72/4 or 18 years.