As quoted from Einstein

"Compounding interest is the eighth wonder of the world".

It's something that isn't intuitive but once you learn it's power it's hard to forget. The lesson comes up again in the story about the Indian ruler rewarding the humble man who invented the game of chess.

Apparently the ruler of India many years ago was delighted with the newly created game of chess. So pleased in fact that he wanted to reward its creator, who as it just so happens was somewhat of a wise man and full on mathematician. (Well what else would you expect from the creator of chess)?

The wise man appeared humble when he asked for simply 1 grain of rice to be placed on the first square of the chessboard on the first day, then double that number of grains of rice on the second square on the next day, and so on until all 64 squares had been filled.

That last number looks like this 9,223,372,036,854,775,808. And the word you're trying to think of is 9 Quintillion. How much money does this equate to? If we assume there are __75,000 pieces of rice in a 2 lb bag__ that costs $2 then one grain of rice costs around $.000027. If we multiply the cost of one grain of rice by the 9 quintillion number above we come out to $245,956,587,649,461 or $245 Trillion!

This is a silly example, but it shows the astounding power of compounding interest. Of course this example is so powerful because he was able to double something 64 times where most investors will only be able to survive long enough to double their investment 5-7 times depending on their returns and lifespan.

### Rule of 72

How does the Rule of 72 correlate with compounding interest and this rice robbery? The Rule of 72 is a shortcut used to estimate the number of years it will take for an investment to double, assuming a fixed rate of annual compound interest. For example, if you have an investment with an annual interest rate of 6%, you would divide 72 by 6% in order to calculate the time to double like this:

72 / 6% = 12 years

Meaning, if you are earning 6% interest on your investments then your money should double in 12 years. We can also look at examples with higher interest rates.

72 / 8% = 9 years

72 / 10% = 7.2 years

72 / 12% = 6 years

### Why 72?

You might be wondering, why 72? Why not 70 or 75? The number 72 works because it’s a convenient approximation that balances simplicity with reasonable accuracy for interest rates typically found in real-world investments (from 5% to 12%). The rule works because 72 is divisible by many common interest rate values (e.g., 3, 6, 8, 9, 12), making the math easier to do in your head. The rule isn’t exact, but for practical purposes, it’s usually close enough.

For smaller rates (e.g., 1-4%), the rule becomes less accurate, but for most everyday scenarios, it gives a reliable estimate.

### Real-World Applications of the Rule of 72

The Rule of 72 is useful for anyone planning long-term financial goals, such as saving for retirement, purchasing a home, or funding education. The most common example would be starting at someone's age with their current savings. Let's say they are 40 years old with $500,000 saved for retirement. If we assume they will retire at age 67 then we have 27 years to compound. If we can grow their assets at 8%/yr then their assets will double every 9 years giving us $4 million dollars by the time they retire.

Age 49 - $1 million

Age 58 - $2 million

Age 67 - $4 million

This is all without saving another dollar.

### Rule of 72 and Debt

The Rule of 72 doesn’t only apply to savings and investments—it’s also relevant when thinking about debt. If you have credit card debt at a high interest rate, you can use the rule to understand how quickly that debt is growing. For example, if you have a credit card charging 18% interest, your debt will double in just four years if you don't make any payments:

72 / 18% = 4 years

This is why paying off high-interest debt as soon as possible is so important. I like to compare the interest rate on any debt I owe with a guaranteed rate in the marketplace. If I can't find a guaranteed rate higher than my debt interest rate then I would strongly consider paying down my debt before investing more.

### Limitations of the Rule of 72

While the Rule of 72 is a handy approximation, it does have its limitations:

**It assumes a constant rate of return**, which isn’t always realistic. Investment returns can fluctuate from year to year.**It’s less accurate at very high or very low interest rates**. For example, with rates below 1% or above 20%, the rule becomes less reliable.**It doesn’t account for taxes or fees**, which can reduce the effective rate of return on your investments.

Despite these limitations, the Rule of 72 remains a valuable and practical tool for quickly estimating the effects of compound interest in a variety of financial situations.

### Conclusion

The Rule of 72 is an easy-to-use and powerful mental shortcut for understanding how your money can grow over time, helping you make more informed financial decisions. Whether you’re investing for the future or managing debt, this simple rule can give you a clearer picture of how compound interest works and the importance of your interest rate. The next time you evaluate an investment opportunity or take a look at your savings, pull out the Rule of 72 to get a quick idea of what the future might hold for your finances.

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