Compound interest is one of the most obvious benefits of long-term investing. Compound interest (the interest that builds upon interest) happens whether or not you add additional funds, but the benefits are even greater when you continue to add funds. But as enjoyable as it is to see the effect that compound interest has on your portfolio, most investors have no idea of what size return they need to reach their goals.
For example, if you have 20 years until retirement, and you have $50,000 in an account that's gaining 6% interest. How many years would it take for you to double your money? How much faster would you be able to double your money if your account gained 8%?
The formula for calculating compound interest would require you to have a calculator that does logarithmic functions. Fortunately, there’s an easier way that gives most investors a statistically significant level of accuracy. It’s called the Rule of 72.
This article will help you understand the Rule of 72 and provide some examples of how it’s used. We’ll also describe some variations of the Rule of 72 that make it useful for a variety of interest rates and circumstances.
What is the Rule of 72?
The Rule of 72 is a simplified equation that can help estimate the number of years required to double the money that is growing at a specified rate of return. It is really as simple as taking the interest rate you are getting and dividing it by 72. Keep in mind, the Rule of 72 works no matter if you’re talking about $50 or $50,000 dollars. The Rule of 72 is only attempting to determine how long it would take to double your money.
When you use the Rule of 72, be sure to enter the interest rate as a whole number, not a percent. So eight percent interest is simply 8, not .08.
Before we go into some examples, I’ll offer a disclaimer. The Rule of 72 is only as accurate as the data that goes in. In many cases, investors will continue to add funds to something like a 401(k), this would greatly reduce the time it would take to double your money because you are adding principal on top of the interest you’re gaining.
Here’s what I mean. If I have $1,000 in a money market account that has an annual interest rate of 5%, the Rule of 72 would say I would double my money in approximately 14.4 years. Here’s how that works:
At the end of the first year (assuming I added no additional money), I would have $1,050. I arrived at that using this simple formula:
(1000 x .05) =50 +100 = 1050
If I simply held unto that money again and added nothing to it, the next year my 5% interest would be based on a principal of $1,050. This means I would gain another $52.50 ($2.50 more than the first year) and I would now have $1,102.50. In two years, I’ve increased the value of my account over 10 percent without adding anything to it. That’s the definition and the benefit of compound interest. You are earning interest on top of your interest because every time the interest is paid out it is being done on top of a principal balance that is higher than before. However, at 5%, you can also see why it would take close to 14 years to double that money.
But what would happen if I were to add an additional $100 at the end of the year? The compound interest at the end of the second year would be based on a new principal balance of $1,150. This would give me a gain of $57.50. And my new balance would be 1,207.50. I’ve effectively doubled the percent gain on my account from just over 10 percent to just over 20 percent. However, even by adding money into my account, the Rule of 72 stays the same. It would still take me 14.4 years to double my new principal balance, not my old balance. Obviously, I would be able to double the value of my account much faster by continuing to make even small deposits.
The other thing to remember is that the Rule of 72 assumes a fixed interest rate. While fixed interest rates may be the norm for some investments like bonds or even money market funds, and may be fairly accurate when it comes to mutual funds and exchange-traded funds. It’s a whole different ballgame when it comes to stocks. If the interest rate goes up or down, it changes the basis for calculating the Rule of 72. In my example if I was now gaining 7% instead of 5% on my $1,000, the Rule of 72 would be as follows:
72/7 =10.2 years
On the other hand, if my interest rate dropped to 3%. The calculation would be:
72/3 = 24 years
To sum it all up: the Rule of 72 is a simplified calculation that provides a realistic estimate for how long it would take money to double assuming the interest rate stays the same. The result of the Rule of 72 does not change if new principal is added, it just applies the rule to the new principal balance.
How accurate is the Rule of 72?
You’ll have to trust me on this, but if you were to do the logarithmic calculation for how long it would take to double the money that was compounding annually at 10%, the number would be 7.3 years. Using the Rule of 72, the number is 7.2. The Rule of 72 is the most accurate between seven and nine percent interest, but it is still quite accurate anywhere between two and 10 percent. This chart shows how statistically accurate the Rate of 72 can be when compared to the actual calculation.
|
Rate of Return
|
No. of Years
(Rule of 72 calculation)
|
No. of Years (logarithmic calculation)
|
Difference
|
|
2%
|
36
|
35
|
1
|
|
3%
|
24
|
23.45
|
0.6
|
|
5%
|
14.4
|
14.21
|
0.2
|
|
7%
|
10.3
|
10.24
|
0
|
|
9%
|
8
|
8.04
|
0
|
|
12%
|
6
|
6.12
|
0.1
|
|
25%
|
2.9
|
3.11
|
0.2
|
|
50%
|
1.4
|
1.71
|
0.3
|
|
72%
|
1
|
1.28
|
0.3
|
|
100%
|
0.7
|
1
|
0.3
|
For investors who are interested in improving the accuracy of the Rule of 72, they can add 1 to 72 for every 3 percentage points that interest rates rise above 9. So that would mean for an interest rate between 10% and 12%, you would use the calculation: 73/(10) or (11) or (12). As you can see on the chart above, dividing 73/12 comes out to 6.08 which is statistically more accurate to the logarithmic value of 6.12.
Conversely, you can subtract one from 72 for every 3 percentage points below 7. So in this case if you had a 5% interest rate, you could use the calculation: 71/5 to get 14.2 which again is statistically more accurate to the logarithmic value of 14.21. For a 2 percent interest rate, the calculation could be 70/2 = 35.
However, these are just suggestions. The Rule of 72 is really just designed to be an estimate for the sake of financial planning. As we’ve previously stated, there are many variables that go into how an investment will grow over time.
Does the Rule of 72 apply only to annualized interest?
The Rule of 72 can be used for any kind of interest: annual, quarterly, or monthly. The calculation becomes only slightly different. For example, let’s say you received 2% quarterly interest on an investment. The time it would take to double your money would be:
72/2 = 36 years
You would then divide 36 by 4 (since interest is paid quarterly – 4 times a year):
36/4 = 9 years
So in this example, you would double your money in nine years. If the interest were paid out monthly, the calculation would be:
72/2 = 36
36/12 (monthly) = 4 years
Other uses for the Rule of 72
You can reverse engineer the Rule of 72 to determine the kind of return you would need from a particular investment. This is particularly critical for long-term planning such as investors planning for retirement. For example, let's go back to our example in the introduction. If you have $50,000 sitting in an account that is earning 8%, you can use the Rule of 72 and you would be able to approximate that you could double your money in nine years (72/8=9).
That means with 11 years left towards retirement, you would have an account worth $100,000. Assuming the same interest rate, it would take another nine years to double that money again. (Remember, the Rule of 72 is agnostic when it comes to the actual amount of money that is in the account.) This means that approximately two years away from retirement you would have a $200,000 account.
Now you have to make a decision. If your goal is to get your account to $500,000 you will need to either increase your principal value or you’ll have to increase your rate of return. If you’re planning on making regular contributions to something like a retirement account, you can run calculations to see how much additional money would be required to help you reach your goal. But using the Rule of 72, you can see that with a 10% interest rate, you could double your money in approximately 7 years. That would mean that you would be at $200,000 with approximately six years left meaning you could have an account closer to $400,000 at retirement. Of course, that introduces significantly more risk into your portfolio, but you can probably find that a combination of regular contributions and a slightly more aggressive portfolio may get you the return you desire.
The bottom line on the Rule of 72
One of the most important reasons to invest is to gain the benefits of compound interest. Anytime you can make money by simply allowing interest to build upon interest, you are maximizing the time value of money. When you’re trying to save for retirement or another major life event, the ability to receive compound interest can be the way to ensure your goal is achieved.
The three main factors that impact the power of compound interest are the interest rate your money is getting, the frequency that interest is compounded (i.e. annually, quarterly, monthly, etc.) and how long the account is compounded. Of these, time is perhaps the most essential and the reason "time is money" is such an apt phrase.
With that said, one of the common questions any investor will ask is how long will it take to double their money? The Rule of 72 is a simple formula that provides an answer that from a statistical standpoint is equal to the actual number that comes from a more complex logarithmic formula.
Using the Rule of 72, you can divide whatever interest rate you are receiving by 72. The answer you get will be the same whether your account value is $50 or $50,000. The Rule of 72 also doesn’t change if more principal is added to the account. The Rule of 72 is only a way to understand the time value of money. From a financial planning standpoint, it can help investors understand if their current plan is on track, if it’s too conservative, or if it’s too aggressive.
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