FLASHCARDS: The Rule of 72 Explained: How Fast Will Your Money Grow?

Gabrielle Birchak/ February 28, 2025/ Late Modern History, Modern History

TRANSCRIPT

It’s Flash­card Fri­day here at Math Sci­ence His­to­ry, and today we’re going to learn a math trick. Have you ever won­dered how long it takes for your invest­ed mon­ey to dou­ble or dis­ap­pear? There’s actu­al­ly a math trick for that. Hi, I’m Gabrielle Birchak.

I have a back­ground in math, sci­ence, and jour­nal­ism, and today you’re going to learn about the rule of 72. Let’s set the scene. Imag­ine you invest a chunk of mon­ey, say $1,000, into an account that earns a steady inter­est rate.

You know that com­pound inter­est is work­ing for you, but you don’t want to pull out a cal­cu­la­tor every time to fig­ure out how fast your mon­ey grows. Enter the rule of 72. It’s a sim­ple for­mu­la that esti­mates how long it takes for an invest­ment to dou­ble, assum­ing a fixed annu­al inter­est rate.

So here’s how it works. Take the num­ber 72 and divide it by your annu­al inter­est rate. The result? That’s the approx­i­mate num­ber of years it’ll take for your mon­ey to double.

For exam­ple, let’s say your mon­ey is earn­ing an 8% annu­al return. With that in mind, we divide 72 by the val­ue of the annu­al return, which is 8, and we get 9. So, since you invest­ed $1,000 at an 8% annu­al return, you should have about $2,000 in about 9 years. There you go.

It’s sim­ple men­tal math. And note that I said 8 and not 8%, because if you were to divide 72 by 0.08, which is the equiv­a­lent to 8%, we would get 900 years, and nobody’s got time for that. So why does it work? Well, the num­ber 72 comes from a log­a­rith­mic for­mu­la for com­pound inter­est, where the pre­cise dou­bling time is cal­cu­lat­ed using nat­ur­al logarithms.

How­ev­er, for sim­plic­i­ty, 72 serves as a close approx­i­ma­tion, offer­ing a quick way to esti­mate dou­bling time for the most rea­son­able inter­est rates. Now, let’s talk about how to use it in real life. The rule of 72 is incred­i­bly use­ful when you’re com­par­ing dif­fer­ent investments.

If a sav­ings account gives you a measly 2% inter­est, we divide 72 by 2, which gives us 36. So, 36 years to dou­ble your invest­ment with 2% inter­est. Hmm, I would­n’t want that kind of an invest­ment, would you? But let’s say you decide to invest in the stock mar­ket, which his­tor­i­cal­ly returns around 7% per year.

Well, with that per­cent­age, the dou­bling time is much bet­ter. So, we divide 72 by 7, and let’s make it eas­i­er. Let’s round down, which is 70 divid­ed by 7. This gives us 10 years.

You’re going to dou­ble your invest­ment in about 10 years. This is why some investors often favor high­er return invest­ments, like stocks, over low-inter­est sav­ings accounts. If you leave your mon­ey in a high-inter­est account or invest­ment fund, you could see mul­ti­ple dou­blings over a lifetime.

Now, what about infla­tion? Well, the rule of 72 isn’t just for invest­ments. It also works in reverse. You can use it to esti­mate how quick­ly infla­tion erodes your pur­chas­ing power.

So, say infla­tion is run­ning at 6% per year. Using the rule of 72, we divide 72 by 6 and get 12. That means in 12 years, the val­ue of your mon­ey will be cut in half.

Dur­ing eco­nom­ic down­turns, inter­est rates tend to drop as cen­tral banks try to stim­u­late growth. That means invest­ments might grow more slow­ly, and dou­bling your mon­ey could take longer. For exam­ple, if an inter­est rate on an invest­ment fell to 3%, using the rule of 72, we find out that 72 divid­ed by 3 is 24.

It would take 24 years for your mon­ey to dou­ble. So, as a quick note, the rule of 72 works best for inter­est rates between 6% and 10%, where it stays with­in about a 5% accu­ra­cy. But if rates are low­er, small adjust­ments can improve accuracy.

I also want to point out that the rule of 72 is just an approx­i­ma­tion, not an exact for­mu­la. For exam­ple, at 2% inter­est, the rule of 70 instead works for a bet­ter esti­mate. At over 10% inter­est, the rule of 74 gives more precision.

For most peo­ple though, stick­ing with 72 is good enough. And if you real­ly want to impress a finan­cial advi­sor, your accoun­tant, your fam­i­ly, or even your friends at a par­ty, use the rule of 72. Because, you know, at a par­ty, noth­ing says a fun time like a smar­ty pants.

Okay, the rule of 72 is a pow­er­ful reminder that time and inter­est work either for you or against you. Invest ear­ly to har­ness expo­nen­tial growth, or risk infla­tion and debt dou­bling faster than your sav­ings. So what can we take away from the rule of 72? Well, first, invest wisely.

Avoid high inter­est debt and hun­ker down to keep up with infla­tion. These are all crit­i­cal for finan­cial suc­cess. Sec­ond, noth­ing in life is guaranteed.

Mar­kets change, economies shift, and unex­pect­ed events hap­pen. Just like your health, your wealth needs reg­u­lar care, smart deci­sions, and a long-term mind­set to thrive. You can do it.

I know you can. Thank you for join­ing me on this Fri­day episode of Flash­cards. That’s all for today on math, sci­ence, history.

If you liked this episode, be sure to sub­scribe and share. And until next time, carpe diem!