What Is The Rule of 72 and Compound Interest (CI)?

If you have ever done any investing, you may have heard about the rule of 72. And, you may be asking “What is the rule of 72?”

Experts often use this rule to compute the period of time needed to save or invest twice as much as investment capital.

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According to the rule of 72, you can find out how fast you can twice increase the value of your capital when your interest rate is divided by 72.

For example, if you get an offer of a 12% interest, this means that you can double your savings if you leave the invested capital alone and don’t touch it for 6 years at the same rate.

Although it’s usually used to compute compound interest rates on savings accounts, it can also be used in many other ways. You can also use it to calculate the duration it takes to pay off a loan!

The formula

What is the rule of 72 and how is it calculated?

It’s really quite simple. The formula is: t = 72/r

Where:

t = time
{r} = % fixed interest rate

How can you apply this mathematical formula in real-life situations? Check out the following use cases with varying interest rates.

ROI is doubled in:

• 72 years if you have a 1% ROI (72 / 1 = 72)
• 24 years if you have a 3% ROI (72 / 3 = 24)
• 12 years if you have a 6% ROI (72 / 6 = 12)
• 8 years if you have a 9% ROI (72 / 9 = 8)
• 7.2 years if you have a 10% ROI (72 / 10 = 7.2)
• 6 years if you have a 12% ROI (72 / 12 = 6)
• 4.5 years if you have a 16% ROI (72 / 16 = 4.5)

It would likely take about 800 years for you to get two times your savings if it were to remain in a regular savings account where it earns between 0.06 and 0.09 percent (the average interest rate on savings accounts nationwide). Therefore, if you have funds you are not using immediately, you are better off investing them in a high-yield savings account, which delivers much greater interest rates, as much as 20 times plus as against the standard average.

How does the Rule of 72 work?

If you are wondering “how does the Rule of 72 work?” you are on the right page. It may look pretty challenging at first but not if you get accustomed to the basic principles.

The rule starts by calculating the future value of a recurring compound rate of return. Anyone who is very cautious when investing isn’t new to this formula, especially when they want to estimate the investment’s exponential growth. It also helps if you want to get insights into possible depreciation.

FV = PV*(1+r)t

When broken down:

FV denotes future value,
PV denotes current value,
r denotes rate, and
t time.

When you include t as the exponent, you can leverage the both-sided natural logarithms to isolate it.

The Rule of 72 calculators can be applied to any annual compounding data, such as macroeconomic data, levy data, and loan data. For example, a GDP growth rate of 4% means that the economy would double in 18 years.

This method can come in handy when you want to determine how long it will take certain funds to double in value, with inflation taken into consideration.

The purchasing power of money becomes 50% less after 12 years with an inflation rate of 6%. You will get the same effect in 18 years rather than 12 years, should the inflation rate hit 4% from 6%.

How accurate is this Formula?

The Rule of 72 is most accurate when fixed interest rates are about 10%, but it gets less accurate when interest rates rise over 10%.

When investing in stocks, it is almost impossible to get interest rates that do not change. The stock market is very dynamic and may not deliver fixed results, especially in the near term.

Having said that, this formula is accurate, particularly when looking at other investment situations where the rates remain constant.

How to use the rule of 72 for your investment planning

You’re probably now wondering when and how to use the Rule of 72. There are several situations in which this straightforward technique might prove beneficial.

If you are looking to make a large transaction, such as investing in a home, you can use it to determine the perfect time to buy it. You can also use it to predict how your other investment options will do.

An excellent example. Investing $50,000 in your child’s college fund requires a return of 7.2% p.a to yield $100,000 within a decade.

However, if your money is $15,000, then it will need to multiply three times in ten years, yielding 21% returns per annum.

Take advantage of the rule of 72 formula and start planning for your retirement as soon as today. Retirement costs can be pretty enormous but even small amounts of money can double if you get things right.

The closer to the age of retirement you get, the higher your investment returns need to be. You may, however, be able to make do with a lower rate if you are far from retiring.

Final thoughts

While we would all like to credit Einstein with coming up with this idea, it wasn’t him. So, who invented the rule of 72?

The first reference of this methodology is found in Luca Pacioli’s Summa de arithmetica 1494. He mentions it in a discussion on estimating an investment’s doubling period.

Make use of this rule to identify viable investment opportunities so that you can reach your financial goals within a reasonable time, especially if you have more time to grow your portfolio.