How to double your money? The Rule of 72!

What Does Rule Of 72 Mean

A rule stating that in order to find the number of years required to doubleyour money at a given interest rate, you divide the compound return into 72. The result is the approximate number of years that it will take for your investment to double.

Others would say, if you want to quickly determine how long it will take for your money to double, the rule of 72 is all you need. Most people generally understand the concept of compound interest, knowing that over time,interest earned will begin to snowball and accumulate more rapidly. Even though it is a relatively simple concept, visualizing how it works can be more difficult.

I think Albert Einstein said it best:

Compound interest is the greatest mathematical discovery of all time.

So, what is the Rule of 72 and what does it have to do with compound interest? The rule simply states that if you divide 72 by the interest rate, it will tell you how long it takes for your money to double. For example, assume you earn a 6% rate of return on your money. To find out how long it takes for your initial amount of money to double, just do the simple calculation:  

72 / 6 percent = 12 years.

It doesn’t matter if you have a starting balance of P500 or P50,000, if you earned a real rate of return of 6% each year, you will double your money after 12 years.

Table of Returns

This table should highlight the importance of squeezing the most out of your money. If you notice, your checking or savings account at the bank earning 1%, by keeping your money there and you’ll need 72 years to double it. But, if you can manage to even get 3% on that money, you can shave 48 years from that goal. Even a modest 7% return will allow you to double your money in just over 10 years.

Even more impressive is when you consider the higher rates of return. For instance, if your investments are in the market during 5 good years and you can realize around a 14% return, you will double your money in that same period.

The Big Picture

For most people, the number of years to double your money seems like a long time. Even at a modest 7% return, that’s just over 10 years. Well, it may seem like a long time, but this is where you have to really take into account the power of compounding over the long term.

Let’s use an example of a 25 year old who has P100,000 saved up in a retirement account. For simplicity, let’s say that the account is earning 14% per year, so according to the Rule of 72, the money will double every 10 years.

Age	Amount
25	100,000.00
30	200,000.00
35	400,000.00
40	800,000.00
45	1,600,000.00
50	3,200,000.00
55	6,400,000.00
60	12,800,000.00
65	25,600,000.00

As you can see, it starts out kind of slow. By age 25, it might not feel like much to have 100,000 saved up. But as the decades pass, the numbers accelerate in value as they double, to a point where by retirement; a measly 100,000 has turned into over P25.6 million. Money begets more money over time.

Also keep in mind, this is simply using a single lump-sum with no additional money being saved. When you consider that most people would be continuously adding money to this investment, the rate of compounding goes up significantly.

More facts

The Rule of 72 is a great [mental math shortcut -> mental-math-shortcuts] to estimate the effect of any growth rate, from quick financial calculations to population estimates. 

This formula is useful for financial estimates and understanding the nature of compound interest. Examples:

• At 6% interest, your money takes 72/6 or 12 years to double.
• To double your money in 10 years, get an interest rate of 72/10 or 7.2%.
• If your country’s GDP grows at 3% a year, the economy doubles in 72/3 or 24 years.
• If your growth slips to 2%, it will double in 36 years. If growth increases to 4%, the economy doubles in 18 years. Given the speed at which technology develops, shaving years off your growth time could be very important.

You can also use the rule of 72 for expenses like inflation or interest:

• If inflation rates go from 2% to 3%, your money will lose half its value in 36 or 24 years.
• If college tuition increases at 5% per year (which is faster than inflation), tuition costs will double in 72/5 or about 14.4 years. If you pay 15% interest on your credit cards, the amount you owe will double in only 72/15 or 4.8 years!

The rule of 72 shows why a “small” 1% difference in inflation or GDP expansion has a huge effect in forecasting models.

By the way, the Rule of 72 applies to anything that grows, including population. Can you see why a population growth rate of 3% vs 2% could be a huge problem for planning? Instead of needing to double your capacity in 36 years, you only have 24. Twelve years were shaved off yor schedule with one percentage point.

When dealing with low rates of return, the Rule of 72 is fairly accurate. This chart compares the numbers given by the rule of 72 and the actual number of years it takes an investment to double.

Rate of Return	Rule of 72	Actual # of Years	Difference (#) of Years
2%	36.0	35	1.0
3%	24.0	23.45	0.6
5%	14.4	14.21	0.2
7%	10.3	10.24	0.0
9%	8.0	8.04	0.0
12%	6.0	6.12	0.1
25%	2.9	3.11	0.2
50%	1.4	1.71	0.3
72%	1.0	1.28	0.3
100%	0.7	1	0.3

Some Caveats

Keep in mind that the Rule of 72 is just a guideline. Clearly, in the real world you’ll almost never have a constant interest rate unless your investment is in a long-term fixed income vehicle. In addition, you will want to consider the impact of taxes and inflation on your results. This rule is simply a tool to help illustrate the impact that time and rate of return has on your money.

Remember, time can be either your greatest asset, or your worst enemy. The sooner you start, even if by just a small amount, it will provide more time for your money to compound. On the other hand, every passing week, month, or year is time that you can never get back. It is up to you to decide if you want time to be on your side or working against you. Hope you learn something new. =)