Computing compound interest using the rule of 72

Calculating compound interest without a calculator can be difficult. Thinking back to my business school days, I remember the formula is something like:

present_value * (1 + interest_per_period) ^ number_of_periods] = future_value

Even if you can remember the formula, calculating 1.08 to the power of 9 is not an easy task to do in your head.

If you do need to do some quick math regarding compound interest, you can easily get a rough estimate of how long it will take any investment to double if you know the rule of 72. A common application for the rule of 72 is: “How long will it take my house to double in value if I assume homes will appreciate at 8% per year?”. To answer this, lets use the rule of 72:

The Rule of 72:

72/annual_interest_rate = number_of_years_to_double_investment

• Dividing 72 by the annual interest rate you expect to achieve over the life of the investment will yield the number of years it will take to double with compound interest.
• Divide 72 by the number of years you want your investment to double, and you’ll end up with the annual interest rate that you’ll have to achieve for your goal to come true.

Using the question above of “How long will it take my home to double in value if I assume appreciation at 8% per year?”, lets apply the rule of 72:

72 divided by 8 (8 percent appreciation) yields 9 years. At 8 percent, your home’s value will double every 9 years.

This is a rough estimate, if you use a calculator to compute the value, you’ll actually end up with your investment having only increased by 199.9004627%, but, its close enough. The rule seems to get slightly less accurate as your interest rate increases, but it is within a few percentage points even as you get near 20%.
Another application of the rule of 72 that I use frequently is: “If I leave my 401k alone right now and don’t deposit any more money into it but can yield 9 percent a year, how much money will I have at retirement?”. Lets use the rule of 72 to figure this out. For this example, lets use the following data:

Your age: 35
Your current 401k value: 100k

At 9% growth, the rule of 72 says your investment will double every 8 years ( 72/9 = 8 ). Starting at the age of 35 with $100,000, I add 8 years and end up with 43. At the age of 43, my 401k will have doubled and would be worth $200,000. Here is the table showing how it will grow until age 67:

$100,000 compounded at 9% per year for 32 years:

35 = 100,000
43 = 200,000
51 = 400,000
59 = 800,000
67 = 1,600,000

If you use the same scenario, but want to compare what happens if you earn say, 12 percent return per year, you use the rule of 72 and say 72/12 = 6, my investment will double every 6 years.

$100,000 compounded at 12% per year for 32 years:

35 = 100,000
41 = 200,000
47 = 400,000
53 = 800,000
61 = 1,600,000
67 = 3,200,000

Using a calculator to compute 9% returns for 32 years, it actually comes out to $1.58 million, pretty close. Using a calculator to compute 12% returns for 32 years, it actually comes out to $3.75 million which is a bit farther off but is mostly due to what I mentioned about higher interest rates causing a higher level of inaccuracy with the rule of 72. Neither numbers are exact, but the rule of 72 works pretty well if you just need a quick estimate.

With the rule of 72, calculating the future value of an investment as it grows over time is simple. Using some basic math, you can impress your friends by quickly calculating the future value of their homes in your head, assuming of course, that your friends would be impressed by that kind of thing.

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