Rule of 72 for Compounding

The ‘Rule of 72’ is a useful means of mentally calculating the approximate annual compounding rate required for money to double over a given number of years. For example, to determine the annual compounding rate required for money to double in six years: 72 + 6 = 12 or 12%. The actual rate is 12.246%.Conversely, if money is invested at 12% per annum compound, dividing 72 by 12 tells us it will take approximately six years for an investment to double in value. For alternate doubling multiples, the equation is: 72 + years × multiplier. For instance, a stock that has increased in price from \$1 to \$6 has doubled 2.5 times (\$2 is once, \$3 is 1.5 times, \$4 is twice, \$8 is three times, so \$6 is 2.5 times). If the time taken to double 2.5 times happened to be, say, 12 years, the annual compounding rate is calculated as: 72 + 12 × 2.5 = 15%. This is the same as dividing 72 by the time it took for the stock to double in price: 12 years + 2.5 times = 4.8; 72 + 4.8 = 15%. The actual rate is 16.1%. Let’s say that someone suggests you should invest in gold because it’s been such a wonderful long-term investment. Leaving aside the fact that the gold price was fixed for over 100 years at US\$20.65 an ounce, its price in 1932 was US\$20.69. The price in the last 72 years has therefore doubled by less than 4.5 times. The annual compounding rate is therefore 72 + 72 × 4.5 = 4.5%. In real money terms, the price of gold has barely kept pace with inflation. Hence, there has been no real capital appreciation in the value of gold over the past 72 years, while its value has deflated over a longer period. The Rule of 72 is useful for doing a quick mental calculation that is not

required to be precise.