# Compound Interest Calculation – the Rule of 72

Call me a nerd, but one of my favorite things to do with money is to calculate compound interest using the Rule of 72. It’s simple math you can do in your head, but it will help you make quick judgments about whether an investment or a loan is going to be worthwhile in the long run.

## How Does Compound Interest Work Again?

Consider how interest works on something many people have: student loans. You were given an interest rate – say, 7% – that magnifies your debt each year it’s unpaid. That means if you took out a student loan today for \$10,000 at 7% interest, then by next year you’d owe the bank \$10,700 – the \$10,000 principal plus the \$700 interest.

If left unpaid, that money will continue to grow, or compound, on this amount. At the end of the second year, your debt will grow to \$11,449. Now it’s not just the principal that’s grown, but the interest itself has compounded, and that’s why we call it compounding interest.

## The Rule of 72: How long does it take for money to double?

The Rule of 72 is easy enough to do in your head – no spreadsheets or calculators required!

The name itself is pretty simple; it’s called the Rule of 72 because you simply divide 72 by whatever your interest rate is

72 ÷ interest rate = number of years before money doubles

This quick calculation gives you a really close estimate on the number of years it’ll take your money to double, no matter how much the principal is.

### The Rule of 72 in Action

Suppose you bought a pizza for \$20 using funds from your student loan, which has an interest rate of, say, 7%. If you divide 72 by 7 (your interest rate) you’ll get 10.3 – the number of years it will take for the cost of that \$20 pizza to double.

72 ÷ 7 = 10.3 years before money doubles

The principle of compounding interest applies to loans and investments alike. While I don’t enjoy calculating how much my debts compound over time, I use it to understand how the interest rate affects the total cost of a loan.

Using the Rule of 72 can also help you size up an investment opportunity. Before investing your money into a savings account that accrues at 2% each year, ask yourself: “How many years will it take for this investment to double in value?” Divide 72 by the interest rate, and you’ll have your answer!

### Compound Interest Rates According to the Rule of 72

Here’s a couple more examples of how that works:

Based on the chart, a savings account that accrues at a 2% interest rate is not a good investment option; you’d have to wait 36 years for your money to merely double. On the flip side, a loan with a 10% interest rate won’t take long at all to become twice as much debt as what you initially took on.

The difference between 2% and 10% is huge – life-changing, in fact. The Rule of 72 will help you make these important assessments quickly and decisively.

## Compound Interest: How much will I have in X years?

There’s another way to calculate compounding interest. Instead of estimating how long it takes for your money to double, you may want to calculate how much it’ll be in a certain number of years. Because this method is more precise than the Rule of 72, it requires a bit more math. You’ll need a basic calculator, like the one on your phone.

Just like for the Rule of 72, you’ll need to know how much interest you expect to earn on average each year. Let’s say the stock market returns an average of 8% annually; by how much will \$1,000 grow each year?

### Calculating Revenue Year by Year

First, to calculate how much the \$1,000 will grow in one year, simply convert the 8% into decimal form (.08) and add 1 (1.08). Then multiply this by the principal, \$1,000 x 1.08 = \$1,080

Revenue after one year = (1+.interest rate) x principal

To account for compounding interest over multiple years, you’ll need to multiply the interest rate on itself, based on the number of years you want to project.

Revenue after multiple years = (1+.interest rate) x (1+.interest rate) x (1+.interest rate)… x principal

For three years of compounding interest at a rate of 8%, multiply 1.08 x 1.08 x 1.08 = 1.259. Then multiply this by the principal.

Revenue after 3 years = (1.08 x 1.08 x 1.08) x \$1,000 = \$1,259

So \$1,000 invested with an 8% return will become \$1,259 dollars in 3 years. Not bad.

### Calculating Compound Interest After 20 Years

To calculate compounding interest after 20 years, start the same way you did above (1.08 x 1.08 = 1.1664). This result is the interest rate you’d use to calculate revenue after the second year of compounding interest.

Now, to reach the interest rate for each subsequent year, you can continue typing [x 1.08 =] over and over again. Or, after doing it once through, you can tap = again for the amount after three years (1.08 x 1.08 = 1.1664 = 1.259). It’s a little shortcut.

From here, tap = 17 more times for the 20-year compounded interest rate of 4.66. Then, multiply this rate by the principal (\$1,000) to equal the total amount of money you would have after 20 years of 8% interest.

So, if your interest compounds at 8% a year on average, then your \$1,000 will become \$4,660 dollars in 20 years

### Another Way to Calculate Compound Interest

If you don’t want to keep track of how many times you need to tap “equal” on your calculator, you can use an exponent instead. This would mean raising 1.08 to the 20th power, using this formula:

Revenue = (1+.interest rate)number of years

Turn your phone sideways and you’ll be able to access a more advanced calculator. Type your interest rate (1.08), then xy, then the number of years (20) and = to get 4.66. This is then multiplied by your principal (\$1,000) for the same result from the example above.

## What’s the point?

Now, why would anyone do this? What’s the purpose of calculating the value of something 10, 20, or 30 years down the road?

It’s appealing to me partly because I’m a money nerd, but I think anyone will find it motivating to see how money grows. With the right kind of interest rate, a small investment today could grow into something significant in the future. Even an amount as little as \$100 can become almost 5 times that, based on this quick compound interest projection.

## The Rule of 72: It Ain’t Rocket Science

You don’t have to be an Einstein to understand compound interest; just use his Rule of 72!

Dividing 72 by your interest rate yields the number of years it will take for your money to double in value. You can use the other compound interest calculations to figure out how much your money is worth in the future based on an estimated interest rate.

Both these methods will help you make better snap judgments in both investing and borrowing. Your brain – and your bank account – will thank you! Tim Fraticelli DPT, MBA, CFP®

Tim Fraticelli is a Physical Therapist, Certified Financial Planner™ and founder of PTProgress.com. He loves to teach PTs and OTs ways to save time and money in and out of the clinic, especially when it comes to documentation or continuing education. Follow him on YouTube for weekly videos on ways to improve your financial health.