What is compound interest and how to calculate it

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

Online calculators, Excel or one formula will help.

What is compound interest

This is the accrual of interest both on the principal amount of investments and on interest for previous periods. The result is similar to the effect of a snowball: it all starts with a small ball, but the further it rolls, the more snow sticks and the larger the ball becomes. Investments of money bring income, and then the latter gives new income - and so on, as long as you have enough patience.

Regular interest works easier: there is a principal amount, on which it is charged once. The difference will be visible even at a one-year distance.

Let's say a person has 100,000 rubles, which he is ready to invest in some asset for a year with 12% profitability during this time. If the income is received only once, then the person will receive 112,000 rubles. And if, for example, interest is accrued every month and is not withdrawn from the account, then by the end of the year there will already be 112,682.51 rubles.

The difference is not so great, but the larger the initial amount, profitability and investment period, the stronger the effect of compound interest.

Where compound interest is used

It is used when you need to calculate the profitability of the most popular asset classes: deposits, bonds and stocks.

In bank deposits

A person can simply put money on a deposit and take profit every year. But banks have enough offers with "interest capitalization" - this is a synonym for compound interest.

For example, a person opens a deposit for 100,000 rubles with a monthly capitalization. This means that in the first month, the profit will be accrued on the original amount, in the second - on the amount with interest, and so on until the end.

Month	Amount at the beginning, rubles	Profit, rubles	End amount, rubles
January	100 000	1 000	101 000
February	101 000	1 010	102 010
March	102 010	1 020, 1	103 010, 1
April	103 030, 1	1 030, 3	104 060, 4
May	104 060, 4	1 040, 6	105 101
June	105 101	1 051, 01	106 152, 01
July	106 152, 01	1 061, 52	107 213, 53
August	107 213, 53	1 072, 14	108 285, 67
September	108 285, 67	1 082, 86	109 368, 53
October	109 368, 52	1 093, 69	110 462, 22
November	110 462, 22	1 104, 62	111 566, 84
December	111 566, 84	1 115, 67	112 682, 51

Suppose that this is only a part of a person's capital, which he is going to transfer from one deposit to another for many years in a row. For simplicity, we will assume that the rate on deposits does not change all this time and remains at the level of 12% per annum.

A person who does not withdraw money, but lets it in for further growth, as a result, will receive one and a half times more. This is important if the plans are long-term - for example, to pay for the education of children in 20 years. Compound interest will help you save more and spend on a higher class university. Or save money and go on a round-the-world trip.

In bonds

Bondholders receive coupons - periodic payments, the dates of which are known in advance. Usually, funds come once a quarter, six months or a year. Coupon amounts, however, are not always announced. Sometimes the interest rate floats, but this is not the most popular type.

If a person does not plan to live on coupon income, then he can reinvest it: get money and buy more bonds with it. The next time, even more funds will be returned - and it will be possible to buy securities again. This is how compound interest starts.

Let's say an investor bought OFZ 29010 for 100,000 rubles. This money is enough for 92 bonds, because they are traded above par on the stock exchange. In a year, the person will receive 59.97 rubles per bond, or 5,517.24 rubles from the entire package.

Then it will be possible to buy five more OFZs. And a year later, the investor will receive 5,817.09 rubles of coupon income. Specialists usually call the mechanism differently - effective profitability. As with deposits, the difference becomes more noticeable over time.

If a person reinvests coupons, he will again receive one and a half times more money. In the case of the example bond, this is almost 116 thousand rubles. Without reinvestment, only 73 thousand will return.

In promotions

Understanding the mechanism for investing in stocks is a little more difficult. If these are growing companies like Yandex, Ozon or Facebook, then the compound interest is, as it were, built-in. Such firms do not pay dividends, but invest all their profits in their development. It turns out that compound interest does not affect the investor's income, but the growth of the company. This means that the share price also grows faster, and a person makes money on this: he bought it cheaper, sold it more expensive.

Other businesses have been around for a long time and have taken a fair share of the market. They have nowhere to grow rapidly, so firms share profits with shareholders through the payment of dividends. Then the investor can run compound interest himself.

For example, a person bought $ 1,000 worth of shares in the communications company AT&T. The firm is called the dividend aristocrat because payments to shareholders have grown continuously for over 35 years in a row. Let's imagine two scenarios: in the first, an investor bought securities 10 years ago, and now he is selling. In the second, it reinvests dividends.

In the first case, a person will lose $ 44.5 on the sale, because securities are slightly cheaper, and if we take into account inflation, then the loss will be even greater. During this time, he will receive $ 523.79 in dividends, which is approximately equal to an average annual yield of 4.3%.

And if an investor does not spend dividends, but buys additional shares of the company with them, then in 10 years he will have 58 securities. This is over 20 more than at the beginning, and there will be more dividends too: $ 665.94 over 10 years. The average annual return in this case is around 5.2%.

In the investment portfolio

Compound interest is not tied to calculations around a single security. It can be applied to the entire investment portfolio.

For example, a person might spend a bond dividend to buy shares in another company. Then make money on the rise in prices, sell shares and use the profit for some other financial transactions. And do it all the time to maintain a good return on investment.

The problem is that it is very difficult to predict the effective return for the entire portfolio.

One unsuccessful sale of stock can reduce the gain from a bargain purchase. Or dividends will suddenly fall due to a bad year for the company, which will also affect the portfolio's profitability.

How to calculate compound interest

This can be done in both easy and time-consuming ways. Let's start with the latter because it's always helpful to understand the mathematics behind finance. Then it will turn out to set goals that are closer to reality.

Manually

Compound interest is primarily a mathematical formula. Its result is the amount that a person wants to receive in the end. Everything is calculated like this:

A = P × (1 + r / n)^nt

The method may sound complicated, but in reality there are only five variables:

• A- amount, that is, the total amount.
• P- principal, initial capital. It can be 100,000 rubles or 1,000 dollars, as in the examples above.
• ris the annual percentage rate that a person expects. For example, a deposit of 12% or an average dividend yield of 5.3%.
• - Periods of interest accrual per year. If they come once a month, then there will be 12 periods a year, and if quarterly - then four.
• t - the number of years for which a person expects to invest.

Suppose that the same bank deposit is chosen: 100,000 rubles at 12% per annum for 5 years, with monthly capitalization of interest. The depositor can calculate how much he will receive at the end of the term:

Step 1	A = 100,000 × (1 + 0, 12/12)(12 × 5)
Step 2	A = 100,000 × (1, 01)(60)
Step 3	A = 100,000 × (1, 817 …)
Step 4	A = 181 669.6 rubles

In five years, the account will have almost double the amount of money. The values may float a bit depending on how long the long numbers are rounded, but the order will remain that way.

If a person took interest every year, he would have on hand the initial 100,000 rubles, plus another 60,000 in profit. The effect of compound interest will bring 21 669 rubles more.

Via a formula in Excel or Google Sheets

Sitting with a calculator or pieces of paper is not interesting for everyone, so the calculation can be entrusted to any spreadsheet. The easiest way to apply is the formula for the future value of an asset. Both Microsoft Excel and Google Sheets call it FV (or BS). It is enough to enter all the initial data in order.

Using the online calculator

Investors and financiers have come up with many free online calculators that calculate compound interest for everything.

For example, for bank deposits, there is or. To calculate coupons on bonds or dividend stock yields, you need more functional options like or. Of the convenient in Russian - and the bank calculator "".

The main problem with all calculations: they are either based on historical data, or they ask a person to guess how the interest rate will change in the future. Therefore, in most cases, this is a way to predict the results of compound interest, but not the fact that it will be so.

What is worth remembering

1. Compound interest is a mathematical formula that triggers the snowball effect. Investing money brings income, and then that gives new income. The longer this goes on, the more a person earns.
2. It is useful to apply compound interest on almost any investment, from a bank deposit to a stock purchase.
3. Compound interest can be calculated manually, in a spreadsheet or on a calculator - it's easy, there are only five variables in the formula.
4. The results of the work of compound interest can only be predicted. Good performance in the past does not mean that a person will earn the same amount in the future.