The Rule for 72

This week, we will be considering the rules of 72

•   You invest #1,000 at a guaranteed 4% interest rate annually. How long will it take your money to double to #2,000?

We can solve the problem by computing compound interest. In the first year, you earn 4% on #1,000 which is #40. In other words, your investment grows to #1,000(1.04) = #1040. In the next year, you earn another 4% on top of #1040, which means your investment grows to #1040(1.04) = #1081.6 which is #1040(1.04)².  Note the pattern, we can see that in X years your investment will grow to #1000(1.04) ^x_.  We can set this equal to #2000 and solve (using logarithms) that x is about 17.67 years. In other words, it takes about 18 years for your investment to double.

The rule for 72 is a shortcut to estimate this answer very quickly. You divide 72 by the interest rate, expressed as a percentage, to get the doubling time.

For example, to calculate the doubling time with a fixed 4% interest rate, we divide 72 by the interest rate of 4%. Since 72/4 = 18, that means the investment will double in roughly 18 years. This is pretty close to the exact answer of 17.67!

Similarly, we can solve an investment with 6% interest will double in roughly 72/6 = 12 years, an investment with 8% interest will double in roughly 72/8 = 9 years, and an investment 12% interest will double in roughly 72/12 = 6 years. These are all very close to the exact answers and the rule avoid having to compute compound interest.

There are two important caveats when using the rule of 72.

First, the rule is a good approximation but it is not an exact answer. When you are working with investments, you may want to check an exact answer with a calculator or spreadsheet.

Secondly, the rule of 72 works only if the interest rate is fixed. When you invest in the stock market, the rate of return varies over time, and so you cannot use the rule of 72 with the same accuracy as you could for an investment with a fixed and guaranteed return.

EXERCISE 

CLICK HERE to attempt some simple questions