# How does compound interest work?

Compound interest is the eighth wonder of the world. Whoever understands it, deserves it; whoever does not pay for it. “- Albert Einstein

This quote is one that many investors are familiar with. It succinctly sums up the power of compound interest and its potential. To fully understand this, you must ask yourself: How does compound interest work?

While many people can explain the function of composition, they are at a loss when it comes to understanding exactly how wealth begets more wealth. Do you know the compound interest formula? Do you know the “rule of 72”? Do you know how much your investments will consist of if you continue to make them on a regular schedule?

These are all questions you need to have the answers to if you are to truly understand the power of compound interest. Read on for these answers.

## What is compound interest?

Compound interest is the interest on an invested balance that increases over time as each recalculation of that balance includes the previous interest payment. The longer the time horizon, the more opportunities there are for capitalization. Likewise, the higher the interest rate, the faster the compound total increases.

To understand compound interest, it’s best to ask a very simple question:

Would you rather have \$ 1,000,000 today or start with a dime and see the balance double every day for 30 days?

This question is popular in beginner personal finance courses. The answer is, of course, the penny doubled for 30 days. Why? Because the magic of compound interest will leave you with a balance of over \$ 10.7 million by day 30 – over 10n times the return on investment of taking the million dollars up front!

While this is an extreme example of 100% compound balance, it nonetheless shows the importance of compound interest. In your retirement accounts, compound interest is a powerful tool to grow your major investments. The earlier you start and the more you contribute, the greater the return on investment.

## An example of composition at work

To get a better example of compound interest, let’s consider a more practical example. Let’s say Bailey invests a lump sum of \$ 50,000 at a fixed rate of 5% per annum. Let’s take a look at how Bailey’s investment grew over different time horizons if she invests an additional \$ 100 each month. After…

• One year, she will have \$ 53,786
• Five years old, she will be \$ 70,968
• 10 years old, she will be \$ 97,878
• 20 years old, she will be \$ 176,735
• 30 years old, she will be \$ 306,611.

For many investors, a six-figure total return on investment is quite achievable through capitalization. With constant contributions, favorable rates of return, and a sufficiently long time horizon, the opportunities for return on investment are virtually limitless.

Want to see compound interest at work for your own investment? Check out our compound interest calculator to see how your contributions are made up over a specific time horizon.

## The compound interest formula

As with all mathematical concepts, compound interest has a formula: P (1 + r / n)NT. In this formula …

• P = the balance of the initial capital
• r = the interest rate
• m = the number of times the interest is applied
• t = the number of elapsed time periods.

As you can see from the raw equation, time plays an important role in the composition. First, the frequency with which a quantity is composed is important to increase the main value. Second, the total amount of time invested (time periods) establishes how many times the balance increases. These two factors together are exponential, which is where the power of compound interest comes from.

## Tips for optimizing compound interest

Believe it or not, there are ways to get the most out of compound interest. This is to manipulate the variables of the above equation.

Take the example of a dividend-paying stock. You can actually double the compounding capabilities of these securities with a Dividend Reinvestment Plan (DRIP). By reinvesting the dividends, you make up your main investment in the number of shares, which pays more dividends. At the same time, when the stock price appreciates, you also gain wealth.

You can also optimize the dialing frequency. For example, you can choose to invest in a fund that is compounded monthly rather than quarterly. This doubles the number of times the interest is applied.

The better you understand how capitalization works, the better you will understand where the opportunities lie to optimize it… and the easier it will be to capitalize on these opportunities within the framework of your preferred investment modality.

## What is the “rule of 72”

The Rule of 72 is a handy little formula this is often used to guess a 100% return on investment. In other words, it estimates how long it will take to double your money. To figure this out, divide 72 by the growth rate of your investment (or interest rate). The result is the number of years it will take you to double your money.

The rule of 72 also works for calculating inflation losses. Divide 72 by the expected inflation rate, and that’s how long it will take for your uninvested dollars to lose half of their value.

## The best investment vehicles for compounding

How does compound interest work? Now that you know the answer, it’s time to use it to your advantage. This means choosing an investment vehicle that offers the best prospects for capitalization. For most investors, this means any type of equity security that offers dividend reinvestment opportunities.