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Notably, you can also flip the equation to find out the fixed interest rate that you need to receive in order to double the present value of your investment. In that case, you would flip the divisor and quotient in the rule of 72, so that our equation would look like this:

*72 / Number of Years = Necessary Rate of Return*

If you were to use the same example from above, you would calculate the following:

*72 / 8 = 9%*

## The history behind the rule of 72

The number 72 works as a mental math estimation because it’s easily divisible by quite a few numbers. In actuality, using the number 69.3 will give you a closer result, but for most people, doing that math would require a calculator.

As for where 69.3 comes from, one of the first known references to the rule dates back to the 1400s. It’s mentioned by Italian mathematician Luca Pacioli in his book *Summa de arithmetica*.

This rule is based off of the time value of money formula, which is:

Future Value = PV × (1+r)n

In this formula:

- PV = Present Value
- R= Interest Rate
- N = Number of time periods

Here, since you’re looking for the value of your investment to double, you would state the future value as two and the present value as one. The equation would look like:

2 = 1 x (1+r)n or, simplified, 2 = (1+r)n

The rule of 72 uses the concept of natural logarithms. In math, a logarithm is the opposite concept of a power. The natural logarithm can be explained as the amount of time needed to reach a certain level of growth with continuous compounding.

To remove the exponent, you need to take the natural log of each side of the equation.

ln(2) = n x ln(1 +r) or ln(2) = r x n

The next step is to divide both sides by the interest rate and, since the natural logarithm of two is equal to 0.693, the equation becomes:

0.693 / r = n

In order to get a percentage, you can multiply the left-hand side by 100%. It leaves you with:

69.3 / r% = n

## Using the rule of 72 in real estate

Truthfully, you can use the rule of 72 in just about every scenario where you would want to estimate compound interest. However, this particular equation is most accurate when the interest compounds annually, which makes it an especially good match for real estate investing and, notably, retirement planning.

While it’s true that you’re not given an interest rate when you invest in real estate in the same way that you would be with credit cards or money market accounts, you can still take steps to calculate your annual return on investment (ROI). Then, you can use that number in place of the compounding interest rate in the rule of 72.

To calculate your rate of return on a real estate investment, you would calculate the following:

*(Gain from investment – Cost of investment) / Cost of investment*

In this case, your gain is from the rental income that you make plus any equity you’ve built. Meanwhile, your cost of investment would represent things like your mortgage payments, maintenance costs, and utility bills.

Once you have all the values in place, you can use this equation to compare how long it will take to recoup your investment with different rental properties.