# What Is Compound Interest ?

Compound interest or interest capitalization refers to adding interest to the deposit amount. As a result, you can further accrue interest on interest by performing a double operation - interest payment and replenishment. Such accrual is used in certain types of bank deposits. In the case of debt, interest is included in the amount of the principal debt. Interest on a deposit with capitalization may be accrued daily, monthly, quarterly, and annually. If they are not paid, then they are added to the deposit amount. And in the next period, interest will be accrued on a larger amount. Now we’re going to find out what is compound interest in more detail.

**How to Calculate Compound Interest**

CI is calculated by using the formula *A = P (1 + r / n) ^{(nt)}*, where:

*A:*In the case of a deposit, it is the total amount that you receive to your account. In the case of a loan, it is the sum that you need to pay off.*P*is the starting amount of deposit or loan.*r*is the yearly interest rate.*n*is how many times a year the interest rate is considered – monthly, quarterly, or annually, depending on the contract and tariff plan.*t*is the number of years for which a deposit or loan is issued.

**What Is the Difference Between Simple and Compound Interest?**

Here are two examples that will illustrate what is the difference between simple and compound interest.

Suppose you took a consumer loan of $1,000 at 10% for 5 years, with recalculation occurring every six months. Therefore:

- P = 1,000
- r = 0.1
- n = 2
- t = 5

In total, during the 5 years you will pay 1,000 * (1 + 0.1/2) ^{(2 x 5)} = 1628. Overpayment will be 1,000 * (1 + 0.1/2) ^{(2 x 5)} – 1,000 = 628. If it was a simple interest, you would have paid $1,500 for 10 years and the overpayment would have been only 500.

Now let’s say that you have invested the same amount at 5% for 2 years, with recalculation taking place every month. Therefore:

- P = 1,000
- r = 0.05
- n = 12
- t = 2

As a result, in 2 years you will have 1,000 * (1 + 0.05/12) ^{(12 x 2)} = 1270. Overpayment and thus profit will be 1,000 * (1 + 0.05/12) ^{(12 x 2)} – 1,000 = 270. If it was a simple interest, your profit would be only $100.

So, an answer to the question “What is the difference between simple and compound interest?**” **would be – it depends on the purpose. Simple interest is better for consumer loans due to low overpayment whereas the compound one is better for investments because of high profitability. For more helpful information on financial terms, refer to the financial dictionary at https://www.enon.com/financial-dictionary

**Benefits of Compound Interest**

Compound interest allows you to earn on interest not only on the initial amount but also on interest accruals accrued earlier. Thus, at the end of each new period, interest is accrued on the entire capital - initial investments plus accumulated interest income.

In our previous example with investment, the CI profit was $270 whereas with a simple interest it would have been $100. Now let’s consider one more example to illustrate how the interest is accumulated with each new period and thus give you a better idea of what is compound interest.

Suppose that you open a $20,500 bank deposit, with an interest rate of 10% for a period of 3 years. The interest is compound and is calculated once a year. For the first year, you will receive an income of $2,500 or 10% of the deposit. For the second year, 10% will be charged on the amount considering the income already received, that is, 0.1 * ($20,500 + $2,500) = $2,300 or 11.2% of the deposit. For the third year, the income will be 0.1 * ($22,300 + $2,300) = $2,460 or 12% of the deposit.

In this example, the total profit will be $7,260 or 33.2% of the initial investment. In the case of simple interest, the income would be 30% or $6,150. The advantage of interest capitalization is obtaining progressive income. The amount of interest that is equal to the ratio of income for the period to the initial amount of investments is rapidly increasing every year.

Like a bank deposit, CI is reflected in trading. A speculative trader seeks to make a short-term profit; therefore, they are looking for instruments with high short-term volatility, the price of which varies greatly during the trading sessions. On the other hand, a trading investor considers long-term investments for a period of several months and years to decades. CI can affect the total income size of both traders, although it plays a more important role for investors.

It is also possible to use CI in futures trading. For example, the current market price of a futures contract is $160,600, and the guarantee for futures is $20,600. Having $45,500, the trader decides to purchase 2 futures for guarantee coverage of $40,500. After two weeks, the price rises by 5%, providing income accrued in the form of a variation margin:

*2 * 160,600 *** 0.05 = $16,060*

The trader gets an opportunity of buying 1 futures contract for $20,600 due to free cash ($4,500) and a variation margin ($16,060). Let’s suppose that after three weeks the futures price increased by another 5%:

*3 * 168,600 *** 0.05 = $25,290*

One-third of the income ($8,430) was provided by futures purchased earlier. Thus, the margin used to buy futures is capitalized, as is the case with dividends or coupon payments. The key difference is that in order to obtain the effect of interest capitalization on futures, the dynamics of its underlying asset should be almost continuously growing.

When implementing this strategy, the trader chooses the period for reinvestment, but not earlier than the moment when the margin with free funds will allow to buy or sell at least 1 futures contract. High risks of the strategy mean that the trader will be able to determine the moment of price reversal and take a profit on time. You can find more information on futures trading at enon.com.

**Summing Up**

**Compound interest** is interest added to the deposit amount with the purpose of accruing more interest. It is a powerful tool for investors and speculative traders, such as futures traders. At the end of each new period, e.g. year, interest is accrued on the entire capital - initial investments plus accumulated interest income.

We hope that now you have a better understanding of what is compound interest and how to calculate compound interest. Check out other helpful glossary articles at enon.com