# The rule of 72

“Compound Interest is the eighth wonder of the world.” – Albert Einstein

Einstein described compound interest as the eighth wonder of the world because he felt that those who understood it, earned it and those who didn’t, paid it. Compounding is what makes saving early and saving regularly such a powerful part of building wealth and it’s also what makes it so hard to get out from under the mountain of consumer debt that so many of us accumulate. In an nutshell, compound interest is earning (or paying) interest on interest. When you earn interest at a compounded rate, your money grows faster because you are earning interest on your total balance (principal + interest) rather than on the principal alone. Similarly, when you pay interest at a compounded rate (as you do with credit cards) your interest charges grow much faster and your debt load gets larger.

Related article: The power of compound interest

We can see the power of compounding in thetable below, which shows how \$1000 earning 5% annual interest grows over time. The first column shows how the \$1000 would grow earning 5% simple interest (earned on just the \$1000 principal)and the second column shows how it would grow earning 5% interest compounded annually (earned on the principal + interest).

 YEAR 5% SIMPLE INTEREST 5% COMPOUND INTEREST 5 \$1,250 \$1,276 10 \$1,500 \$1,629 15 \$1,750 \$2,079 20 \$2,000 \$2,653 25 \$2,250 \$3,386 30 \$2,500 \$4,322 35 \$2,750 \$5,516 40 \$3,000 \$7,040 45 \$3,250 \$8,985 50 \$3,500 \$11,467

## The rule of 72

The rule of 72 is a simple way to estimate how long it will take your money to double in value at a given interest rate. If you divide 72 by the annual interest rate, the answer is the number of years it will take to double. For example, 72 divided by 5 is 14.4. This means that, as you can see in the table above, it takes just under 15 years for \$1,000 to become \$2,000. 15 years later (in year 30) the money has doubled again to be just over \$4,000 and, 15 years after that (in year 45) it has doubled again to become more than \$8,000. In year 60, it will have doubled yet again and become \$16,000. Using this rule, it’s clear to see that both time and interest rate are two key factors in building wealth. At 8% interest, your money will double in 9 years (72 divided by 8 = 9) but it will take 36 years to double earning 2% interest. For a 20 year old, \$100 invested at 7% is worth \$2,100 at age 65. For a 30 year old, that same \$100 invested at the same rate is only worth \$1,068 at age 65 and for a 40 year old, \$100 invested at 7% is worth just \$543 at age 65. This means that, at 40 years old, even though I’m only twice the age of the 20 year old, I have to save four times as much each year in order to achieve the same level of wealth at age 65. It’s a concept that I wish I had understood as a teenager because I’m pretty sure it would have motivated me to manage my money differently!

Related article: Pay Yourself first is the best way to save

At the end of the day, saving is always a very personal decision: the choices we make about whether to save, where to save and how much to save, vary enormously from person to person. However, all too often, I hear people in their twenties saying that they’ll wait to save until they’re older because then they’ll be earning more. When you consider how powerful a factor time is in the wealth building equation, it just doesn’t make sense (especially when you consider that just because you’re earning more doesn’t mean you have more discretionary income). If you can do as much with \$25 at 20 as you can do with \$50 at 30 or with \$100 at 40, it makes sense to start the saving habit early.

Related article: Principles of Saving money

Even if you feel like you’ve “missed the boat” because you should have started saving years ago, remember that whatever you save today has a greater power to grow than money you save next month, next year or 3 years from now. We can’t change our past choices but we always have the power to choose to change our financial future by making different choices today.

1. Doug Runchey

Sarah

I think you might want to check the math for your “5% simple interest column”. Each 5-year period should accrue \$250 of interest, not \$50.

2. Sarah

Yikes! Thanks Doug. I fixed it : )

3. irene

Sigh, now if only I could find out where to get 5% interest! Maybe the example should have used 0.5% interest

4. Sarah

Hi Irene, You’re right about a guaranteed 5% return being hard to come by. We’ve come a long way from the high rates of the early 1980s! However, if you’re investing your money then there are a lot of mutual funds that have averaged at least 5% a year over the past 5-10 years. What the markets will do going forward is impossible to predict but if you can keep your MERs low that will definitely help improve your returns.

5. Peter

Hello Sarah

Love your article, hate the errors i.e.:
“In an nutshell, compound interest is earning (or paying) interest on interest. When you earn interest at a compounded rate, your money grows faster because you are earning interest on your total balance (principle + interest) rather than on the principle alone.”

All of the above mentioned “PRINCIPLE(S)” really refer to “PRINCIPAL(S)”.

I’m very surprised that you would not know that

6. Sarah

Peter, thank you SO much for pointing that out. I have no idea how I missed that – it will get fixed right away! I’m glad that you liked the article.

7. Jimmy

OMG, who gives a rats about very minor grammar mistakes. These people provide us with AMAZING information and pieces to help our business and clients. Give it a rest Peter and go grab a beer! Sarah, keep up the KICK ASS work!

• Sarah

Thanks Jimmy! I’m really glad you like the site and the information : )

8. Claude Mayrand

Sarah,

The rule is strictly applicable to compound interest when the earned interest is also subject to the same interest.

It shouldn’t be used for dividends for instance or even interest on bonds, because the dividends/interest are typically not reinvested.

For dividends, normal math applies. 6% per year would accumulate to double the capital in (100%÷6)=16.67 years rather than (72÷6)=12 years.

9. Peter

Your comment, Claude, underscores and reiterates the reason why dividends should be reinvested.