# Compound Interest – How to Calculate with Examples

## How to Calculate Compound Interest with Examples

This tutorial explains what compound interest is and how to calculate it.

### What is compound interest?

If you want to increase your assets even a little for when you need a large amount of money, time deposits and mutual funds will be one of the options.

If you want to invest intending to increase your assets, I recommend choosing a financial instrument with a compound interest calculation method, which incorporates dividends into the principal.

Instead of receiving dividends regularly like simple interest, compound interest increase the principal by incorporating interest into the principal, making it easier to increase assets than simple interest.

Compound interest is a method of calculating interest by adding the interest accrued over a certain period to the principal and then using the principal and interest as the principal when interest is generated next time. You will be charged more interest on interest.

Unlike simple interest, the interest generated can be incorporated into the principal, so the longer the investment period, the more the total interest amount becomes the point of compounding. In addition, compounding interest can be expected to further increase your assets by shortening the incorporation period.

For example, with simple interest, if the annual interest rate is the same, there is no difference in the total amount of interest received, whether the maturity is six months or one year.

### Compound interest: how to calculate

Calculation methods and formulas

So what is the interest formula for calculating the increase in assets when you invest using compound interest?

The following formula, which uses the principal amount, annual interest rate, and the number of years of operation, is used to calculate the assets.

Assets when compounded = principal × (1 + annual interest rate)^n, where n is years of operation.

You can calculate how your assets will grow in the case of compounding by adding one and the annual interest rate, multiplying it by the number of years of operation, and then multiplying it by the principal.

For example, if the principal is \$1,000,000 and the annual interest rate is 5%, the amount will be \$1,050,000 in the first year.

= \$1,000,000 × (1 + 0.05)^1 = \$1,050,000

Further the following year and continue to compound interest operation as the principal of this \$1,050,000, in the 2nd year it will be \$1,102,500.

= \$1,000,000 × (1 + 0.05)^2 = \$1,102,500

On the other hand, in the case of a simple interest investment, assets are calculated by the following formula:

Assets invested at simple interest = principal x (1 + annual interest rate x n), where n is the number of years of operation.

In the case of a simple interest operation, the interest will be \$50,000 for the second year, which means that after the 2nd year, the compound interest operation will increase the asset faster.

With compound interest, if the operation goes well, the asset will increase rapidly like a snowball.

Let's take a look at another example:

For example, the principal is \$1,000,000, and if you deposit this \$1,000,000 at an annual interest rate of 2% for one year, it will be \$1,020,000 after one year. In this case, \$20,000 is the interest attached to the principal. Including this \$20,000 (i.e., \$1,020,000), once again interest rate 2% in another one year deposit, it becomes \$1,040,400, not 1,040,000. This \$400 is an interest on 20,000, which is interest. In this way, it is called compound interest that interest is also attached to interest.

In the long term, the effect of compound interest is very significant. It is necessary to incorporate interest into the principal amount and operate it to make compound interest. In the above example, \$20,000 of interest was added to \$1,000,000 of principal, and \$1,020,000 was used as a new principal.

On the other hand, if the interest is not incorporated into the principal amount, it becomes a simple interest. In the above example, if \$20,000 of interest is not incorporated into the principal of \$1,000,000, and only \$1,000,000 is deposited again at 2% interest, the amount after one year would be \$1,040,000 (\$1,000,000 + \$20,000 of interest in the first year + \$20,000 of interest in the second year). This kind of investment is called a simple interest investment.

In addition, if you borrow money and cannot pay it back, the interest on the debt will also accrue, and the debt will increase with compound interest.

### Summary

Compound interest calculation is one of the methods of calculating interest and interest rates. Unlike simple interest, which allows you to receive dividends periodically, interest and rates are incorporated into the principal.

The compound interest is recommended for those who want to increase their financial assets through mutual funds or deposits, as the amount of interest and the amount that is the basis of interest rate calculation will increase. On the other hand, if you choose the compound interest type for borrowing money, such as a loan, the principal amount will not decrease forever, and you may have a hard time repaying the loan.