What is the rule of 72, and how long does money take to double at 9% compound interest?
Doubling time is roughly 72 divided by the annual rate in percent. At 9% that is 72 / 9 = 8 years. The exact answer is log 2 / log 1.09, about 8.04 years, so the rule is very close.
Explain it simply
Compound growth is hard to do in your head, so investors use a quick estimate: divide 72 by the interest rate to get the years needed to double. A fixed deposit at 6% doubles in about 12 years; a fund growing at 12% doubles in about 6. It is an approximation that works well between roughly 6% and 12%.
Example
Question: At 9% p.a. compound interest, how long does ₹50,000 take to double?
- Rule of 72: 72 / 9 = 8 years.
- Check: 50,000 x (1.09)^8. Since 1.09^2 = 1.1881, 1.09^4 = 1.4116, 1.09^8 = 1.9926, the amount is about ₹99,630. Almost exactly double.
- Exact time: log 2 / log 1.09 = 0.6931 / 0.0862, about 8.04 years.
console.log((Math.log(2) / Math.log(1.09)).toFixed(2)); // Output: 8.04
console.log(Math.round(50000 * Math.pow(1.09, 8))); // Output: 99628A related exam fact: at CI a sum that doubles in n years becomes 4 times in 2n years and 8 times in 3n years.
What to say in the interview
"The rule of 72 says the doubling time is about 72 divided by the rate. At 9 percent that's 8 years, and the exact log answer is 8.04, so it's a reliable mental check. At compound interest, 8 times takes three doubling periods."
Common mistakes
- Applying the rule to simple interest, where doubling takes 100 / R years.
- Expecting it to be exact; it drifts at very high or very low rates.