The Rule of 72
I just read about a study showing remarkable levels of financial ignorance about compound interest. A samp
le of 1000 consumers were asked, if they had a credit card balance of $1000 at 20% interest and they made no payments, how long would it take for their balance to double. Only 36% of all adults answered correctly – and alarmingly only 26% of women answered correctly.
There is an urban legend that Albert Einstein once described compound interest as “the most powerful force in the universe”. Yet two-thirds of adults do not understand how it works or how it impacts their lives. I do not want my daughters to grow up with this kind of ignorance about finance.
When I was about ten years old, my grandparents gave me a book about personal finance.
One concept that I found fascinating and have always remembered is “The Rule of 72”.
The Rule of 72 helps you calculate how many years it will take for money to double at a particular rate of compound interest. Before we look at the Rule of 72, here’s a brief overview of how compound interest works. Compound interest is different from simple interest.
Simple interest applies the interest rate to the loan balance only. Let’s say you borrow $100 at simple interest of 10% per year. At the end of the first year, you will owe $10 in interest, plus the original $100 you borrowed. If you continue to borrow the $100 for a second year, you will owe another $10.
Compound interest is “interest on interest”. If you borrowed $100 for two years at 10%, after the first year, your balance would be $110 (the initial $100 plus $10 interest). The second year, you pay 10% interest on the $100 loan amount PLUS 10% interest on the $10 interest from the first year. So your total interest for year two is $11 (or 10% of $110).
If you keep going at a 10% interest rate, you’ll find that after seven years, the $100 loan balance will compound to $200. I remember as a kid working out this rule by hand. I literally did the compounding 7 times to see if it worked. Pretty amazing.
So how does the Rule of 72 work? Divide 72 by the interest rate. If the interest rate is 10%, then divide 72 by 10. The answer is 7.2 years. If your interest rate is 4%, then divide 72 by 4. The answer is 18 years.
The Rule of 72 is an example of a Rule of Thumb – a guideline for making a guess, but not always accurate in all situations. (Academics like to call Rules of Thumbs “heuristics” – which is a way of solving problems based on experience, intuition, or educated guesses.)
So where does the rule of 72 not work? It works best when the interest rate is close to 8%. For an interest rate below 8%, the Rule of 72 overstates the time to double (it will actually take less time. For interest rates above 8%, the Rule of 72 understates the time to double (it will actually take more time.)
Some key lessons here:
1. Learn how compound interest works. It can help you immensely as an investor and can harm you immensely as a debtor.
2. Whenever someone suggests a “rule of thumb” – understand the circumstances in which it useful and accurate or not.
If you’d like to play around with a simple spreadsheet I created to illustrate the Rule of 72, click here.
