 # What is compound interest? | The Motley Fool

When it comes to calculating interest, there are two basic choices: simple and compound. Simple interest simply means a fixed percentage of the principal amount each year. For example, if you invest \$1,000 at 5% simple interest for 10 years, you can expect to receive \$50 in interest each year for the next decade. No more no less. In the investment world, bonds are an example of a type of investment that typically pays simple interest.

On the other hand, compound interest is what happens when you reinvest your income, which also earns interest. Compound interest basically means “interest on interest” and that’s why many investors are so successful.

Read more: Simple Interest vs Compound Interest

Think of it this way. Let’s say you invest \$1,000 at 5% interest. After the first year, you receive an interest payment of \$50. But, instead of putting it in your pocket, you reinvest it at the same rate of 5%. For the second year, your interest is calculated on an investment of \$1,050, or \$52.50. If you reinvest this, your third year interest will be calculated on a balance of \$1,102.50. You had the idea. Compound interest means that your principal (and the interest it earns) grows over time.

The difference between simple interest and compound interest can be huge. Watch the difference on a \$10,000 investment portfolio at 10% interest over time:

Period of time Simple interest at 10% Compound interest (annually at 10%)
To start up \$10,000 \$10,000
1 year \$11,000 \$11,000
2 years \$12,000 \$12,100
5 years \$15,000 \$16,105
10 years \$20,000 \$25,937
20 years \$30,000 \$67,275
30 years \$40,000 \$174,494

Author’s calculations.

It is also worth mentioning that there is a very similar concept called cumulative interest. Accumulated interest refers to the sum of interest payments made, but it generally refers to payments made on a loan. For example, interest accrued on a 30-year mortgage would be the amount you paid for interest over the term of the 30-year loan.

## How compound interest is calculated

Compound interest is calculated by applying an exponential growth factor to the interest rate or rate of return you are using. To calculate compound interest over a period of time, here is a mathematical formula you can use:

Where “A” is the final amount, “P” is the principal, “r” is the interest rate expressed as a decimal, “n” is the compounding frequency, and “t” is the period in years. Here is what all these variables mean:

• Main refers to the starting balance on which interest is calculated. The term is most commonly used in the context of the initial balance of a loan, but can also apply to your initial investment amount. For example, if you decide to invest \$10,000 for five years, that amount will be your principal for compound interest purposes.
• Rate refers to the interest rate (or the expected rate of return on an investment), expressed as a decimal. For calculation purposes, if you expect your investments to grow at an average rate of 7% per year, you would use 0.07 here.
• Dialing frequency refers to how often you add interest to the principal. Using the example of 7% interest, if we were to use annual compounding, you would simply add 7% to the principal once a year. On the other hand, semi-annual capitalization would imply applying half of this amount (3.5%) twice a year. Other common dialing frequencies are quarterly (four times a year), monthly, weekly, or daily. There is also a mathematical concept called continuous compounding, where interest is constantly accumulating.
• Time is a fairly self-explanatory concept, but for the purpose of calculating compound interest, be sure to express the total period in years. In other words, if you’re investing for 30 months, be sure to use 2.5 years in the formula.

## Dialing frequency makes the difference

In the previous example, we used annual compounding, which means that interest is calculated once a year. In practice, compound interest is often calculated more frequently. Common dialing intervals are quarterly, monthly, and daily, but there are many other possible intervals that can be used.

Dialing frequency makes a difference – in particular, more frequent dialing leads to faster growth. For example, here is the growth of \$10,000 at 8% compound interest at several different frequencies:

Time

Annual composition

Quarterly

Monthly

1 year

\$10,800

\$10,824

\$10,830

5 years

\$14,693

\$14,859

\$14,898

10 years

\$21,589

\$22,080

\$22,196

Read more: Which accounts earn compound interest

## Example of Compound Interest Calculation

As a basic example, let’s say you invest \$20,000 at 5% interest, compounded quarterly, for 20 years. In this case, “n” would equal four since quarterly capitalization occurs four times a year. From this information, we can calculate the final value of the investment after 20 years like this: ## Compound Profit vs Compound Interest

The difference between compound interest and compound income is that compound income refers to the compounding effects of both interest and dividend payments, as well as appreciation in the value of the investment itself.

For example, if an investment in stocks gave you a dividend yield of 4% and the stock itself increased in value by 5%, you would have a total profit for the year of 9%. When these dividends and price gains accumulate over time, it is a form of compound income and not interest (since not all gains come from payments made to you).

In a nutshell, when you’re talking about long-term returns from stocks, ETFs, or mutual funds, it’s technically called compound earnings, although they can still be calculated the same way if you know your expected rate of return.

## Why compound interest is such an important concept for investors

Compound interest is the phenomenon that allows seemingly small sums of money to grow into large sums over time. In order to fully leverage the power of compound interest, investments must be able to grow and accumulate for long periods of time. 