My Blog, Your Money

In my last post, I wrote about the power of compound interest. This week, I wanted to go over the rule of 72 (also known as the rule of 70). Basically, it is a rule of thumb for calculating the length of time it will take an investment to double. Here’s how it works: Just divide 72 or 70, whichever number is more convenient, by an expected rate of return and the quotient is the approximate number of years it will take for an investment to double.

Example time: let’s say you invested $10,000 in the stock market and expected a 9% return each year. Since 72 ÷ 9 = 8, it would take 8 years to double the initial amount of $10,000 to $20,000. That’s all there is to it.

Similarly, you can also apply the rule to calculate the effects of inflation on your purchasing power. If you assume that inflation increases at 3% annually, then in 72 ÷ 3 = 24 years, your purchasing power will be half of what it is now. It is half because inflation decreases the value of your money over time. If your expectations are close, then this could serve as a good way to calculate how much money you will need to retire.

Here is a table that compares the values estimated by the rule to the actual number of years required:

Some of you may think this is a neat little trick, but then gripe that your long-term goal is not to just double your money. At least I hope it isn’t. As the previous post indicated, allowing wealth to grow exponentially through the power of compound interest is a process that takes time. Most likely, you’re not going to invest your money for 8 years and then be ready for retirement. You’ll probably be growing your money over several decades before you are ready to retire and enjoy the fruits of your labor.

So, with that being said, you can take the rule a little bit further and link up a chain of doubling periods. For example, let’s say Bob just graduated from college at the age of 22 and will work until the age of 59 ½ (the age you may make withdrawals from your IRA/401(k) without incurring early withdrawal penalties). After 1 ½ years of working, Bob is now 23 ½ and has saved up $10,000 which he decides to invest in the stock market. On average, he expects a 12% annual return. 72 ÷ 12 = 6 so it would take 6 years for his money to double…once. Bob is patient though and he’ll leave the money there until he retires. Given that he’ll retire at the age of 59 ½ and he started investing at 23 ½, the money will be allowed to grow for 59 ½ – 23 ½ = 36 years. Since it will take 6 years for his money to double, within that period of time, the money will double 6 times! (36 years ÷ 6 years to double= 6 times doubled). Now how much would Bob’s initial $10,000 be if he doubled it 6 times? It looks like we’re going to need an exponent (which is your best friend in a situation like this): 2⁶ = 64. So in 36 years, he will have 64 times his initial investment of $10,000 or $640,000. That’s a decent chunk of change.

Furthermore, for most people, their retirement plans don’t consist of just investing one deposit of money until they retire. Most people would sock away money every now and then as their income rises from raises and bonuses. So, an initial investment is just the beginning. Hopefully, it becomes a habit and you are able to save money routinely. For those who do save a specific amount of money periodically, there’s an extension of the rule of 72 that allows you to calculate the future value of an annuity (a series of equal payments) known as Felix’s Corollary. I don’t want to go into it in depth here as it’s a bit more complicated, but if you are interested in learning more about it, I suggest visiting the link.

Here are some additional resources for those interested in learning more about the rule of 72:

The Rule of 72 at Wikipedia: Detailed explanation and derivation of the rule, describes E-M Rule and Felix’s Corollary

Better Explained – The Rule of 72: Overview of the rule including a derivation of the formula for those math geeks out there