Double Your Money: Rule of 72

A few weeks ago, one of my students came to me just before lunch and asked, “can we talk about the Rule of 72?” Of course my heart fluttered with joy because a kid was actually asking me to teach them something mathematical. “Sure!” I said, “What specifically do you want to know?” She smiled, “well – like – what is it? I was at this party with my friends and her parents and the people presenting asked us if we learned about all these different money things in school and the one thing I remember was ‘the Rule of 72.'”

So we sat down and learned the Rule of 72. It’s very simple: the rule let’s us estimate how long it will take money to double its current value. I never fully appreciated this tool because I prefer precision and I always sit down with the actual compound interest formula to calculate based on my timeline. I never used the Rule of 72 in any planning of mine because the rule gives you the timeline and I’d rather plan for my preferred timeline. The rule let’s you estimate time based on your rate of return. You just divide 72 by the rate and it gives you the time.

So for example, if you expect a rate of return of 8%, your time to double would be 9 years:

If you expect a rate of return of 9%, your time to double would be 8 years.

If you expect a rate of return of 10%, your time to double would be 7.2 years.

It’s a really nice rule that is fairly simple for sketching out some plans. The problem is, of course, that you can’t predict what rate you will earn unless you have a CD, rates of which currently hover at 2% or below. A rate of 2%, according to this rule, means your money will take 36 years to double in value. Note, also, that the rule becomes less precise as you move further away from 9%. So for low rates like 3% or high rates like 16%, it doesn’t work as well.

What we did next is why I really started to like this rule. My student then asked “Is that what that one guy was talking about when he said we could have 2 million dollars by the time we retire?” Earlier in the year one of our guest speakers encouraged students to plan and to save now, when they are young because of the beauty of compound interest. A cool example is that if an 18 year old saves $2000 a year for the four years they are in college, they can have $2,000,000 by the time they retire. She wanted to know exactly how. So we did the following math together.

Assume we just start calculating at age 22 when she’s saved $8000. What we can do is calculate how many doubling periods we’d need to reach $2 million or more. So we doubled $8000 until we got there:

Each arrow is a period of doubling. It would take 8 doubling periods for that money to break the $2 million level. So now what we need to do is determine how long a doubling period is and then determine how old she’ll be after the 8 doubling periods. We need the Rule of 72 to calculate how old she will be when she can retire with her desired $2,000,000.

If she earns a rate of 8%, the doubling period is 9 years. So at 9 years * 8 doubling periods, it would take 72 years of patiently waiting for the money to be $2,048,000. She would be 84 years old. That’s kind of old. My student made it quite clear that she did not want to work until she was 84.

If she earns a rate of 10%, the doubling period is 7.2 years. So at 7.2 years * 8 doubling periods, it would take 57.6 years of waiting. She would be 79.6 years old. That’s better but not by much.

If she earns a rate of 12%, the doubling period is 6 years. So at 6 years * 8 doubling periods, it would take 48 years for her money to double. Now she is 70 years old when she can retire.

Some people do expect to retire when they are 70 years old. But you can retire on social security at 62.5 years old. My student pondered a good retirement age and said, “well can’t I just retire one doubling period early with $1 million?” Of course you can! Having $2 million isn’t going to be necessary. With her 12% rate that means she’d only need 42 years of doubling which would make her 64 years old. That’s much more reasonable. Remember that in this example, she only saved $8000 in total. She could save more to have a higher ending balance. It was just an example we used to explore the Rule of 72.

The 12% actually the rate that Dave Ramsey uses when he writes about this on his blog. He says that if you invest $2000 for 8 years starting at age 19, you will have more than half a million more at age 65 than a person who saves $2000 a year starting at age 27 and never stops saving.

The point is that the earlier you start, the better off you will be. You give yourself more doubling periods and you don’t have to save as much out of your own pocket. However, 12% is a very aggressive rate and many people won’t actually earn this rate. You have to be comfortable with more risk, meaning more dips in your account value. When using the rule of 72, use numbers from 6% to 9% for your estimates. The last thing my student asked me is “What do you do?” referring to the rate that I earned. When we meet again and discuss this, I will let you know what we learned!

 

 

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