Albert Einstein called compound interest the 8th Wonder of the World, but a high rate of interest can work for you or against you. When you invest, it works for you. When you borrow, it works against you.
The Rule of 72 is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to double, or if you are borrowing money, how long it will take to double your debt if you don’t pay down your principal.
For example, the rule of 72 states that $100,000 invested at 10% would take 7.2 years ((72/10) = 7.2) to turn into $200,000. In actuality, a 10% investment will take 7.3 years to double ((1.10^7.3 = 2). Close enough for a rule of thumb.
When dealing with low rates of return, the Rule of 72 is fairly accurate. This chart below compares the numbers given by the rule of 72 and the actual number of years it takes an investment to double.
Notice that, although it gives a quick and dirty estimate, the Rule of 72 gets less precise as rates of return become higher. Therefore, when dealing with higher rates, it’s best to calculate the precise number of years algebraically by means of the ‘future value’ formula.
You can see that it makes a big difference how many times your money doubles. If you can make it double only a few more times by making just slightly better investments, you can end up with many times more money at retirement or whenever you need it. ($1… $2… $4… $8… $16… $32… $64… $128)
You should keep the Rule of 72 in mind too when you decide to purchase a CD from your bank at 1.0% APY for 9 months. Your actual return is closer to 0.75% as APY = annualized percentage yield, not your true yield, and at that rate, you will double your money in 96 years. Live long and prosper and pray that inflation is a thing of the past.
Eric Linser, CFA
Aug. 10, 2009