# 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 earns simple interest.

On the flip side, compound interest is what happens when you reinvest your earnings, which also earns interest. Compound interest basically means “interest on interest” and this is the reason why many investors are so successful.

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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, which comes to \$ 52.50. If you reinvest this, your third year interest will be calculated on a balance of \$ 1,102.50. You got the idea. Compound interest means that your principal (and the interest it earns) increases over time.

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

Period of time Simple interest at 10% Compound interest (annually @ 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

Calculations by author.

It should also be mentioned that there is a very similar concept known as cumulative interest. Accumulated interest refers to the sum of interest payments made, but generally refers to payments made on a loan. For example, the interest accrued on a 30-year mortgage would be the amount you paid for interest over the life of the 30-year loan.

## How is compound interest calculated

Compound interest is calculated by applying an exponential growth factor to the interest rate or rate of return you use. To calculate compound interest over a certain 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 the meaning of all these variables:

• Main refers to the starting balance on which interest is calculated. The term is more commonly used in the context of the initial balance of a loan, but can also apply to the amount of your initial investment. For example, if you decide to invest \$ 10,000 for five years, that amount will be your principal for purposes of calculating compound interest.
• Rate refers to the interest rate (or expected rate of return on the 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.
• Compound frequency refers to how often you add interest to principal. Using the example of a 7% interest, if we were to use the annual compounding, you would just add 7% to the principal once a year. On the other hand, the half-yearly composition would imply applying half of this amount (3.5%) twice a year. The other common dialing frequencies are quarterly (four times a year), monthly, weekly or daily. There is also a mathematical concept called continuous composition, where interest is constantly building up.
• Time is a pretty self-explanatory concept, but for the purposes of calculating compound interest, be sure to express the total period in years. In other words, if you are investing for 30 months, be sure to use 2.5 years in the formula.

## The compound frequency makes the difference

In the previous example, we used annual compounding, which means 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.

The frequency of compounding makes a difference – in particular, more frequent compounding results in faster growth. For example, here is the growth of \$ 10,000 at an interest rate of 8% compounded 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

## Compound interest calculation example

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

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

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

In short, when you talk about long-term returns on stocks, ETFs, or mutual funds, it’s technically called compound earnings, although it can still be calculated the same way if you know your rate. expected return.

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

Compound interest is the phenomenon that allows seemingly small amounts of money to grow into large amounts over time. In order to take full advantage of the power of compound interest, investments must be able to grow and compound over long periods of time.