Compound interest on deposits. Compound interest formula

Each of them relates to deposits in its own way: some prefer to accumulate money in bank accounts, while others sleep easier when they understand that all the money is under their pillow.

Banks help earn money on their own money - they offer cash rewards in the form of accrued and paid interest for each issued savings account.

If you decide to entrust your savings to a bank, then first of all you need to understand how much you can earn, which bank is more reliable and on what conditions it offers deposits.

In this article, we will focus on the question of what constitutes a compound interest on deposits, and how to calculate it.

Differences from Simple Interest

There are two types of interest on deposits or deposits - simple and complex. We can’t talk about the first of them for a long time, since a simple percentage is pretty easy to calculate.

Compound interest is a type of accrual that increases the size of the deposit body by its size without breaking the deposit agreement. It is also called a capitalization deposit.

That is, at a rate of 20% with capitalization, the condition that at the end of the period you will receive the same percentage more money does not apply.

Benefits with Compound Interest

Banks are not profitable with such deposits, as they have to pay more for the use of borrowed funds. Therefore, interest rates on them are often an order of magnitude lower than those of deposits that involve simple accrual of interest.

Most often, a complex percentage is presented in deposits with the possibility of constant replenishment. Sometimes banks try to lure customers into deposits, from which you can withdraw or invest money at any time. But interest rates for the second type are significantly lower than in deposits that do not imply a partial withdrawal.

What is the compound interest formula?

So, having understood the essence of the concept, we will proceed to the implementation of practical calculations.

Suppose you want to place 200 thousand rubles in a deposit. The choice fell on the deposit, which implies the accrual of complex bank interest with a level of 11% per annum.

Deposit conditions include monthly interest capitalization. This means that the amount of interest that is due to you for depositing within a month will be calculated and added to the total amount of the initial deposit. And from next month, interest will be calculated on a new deposit amount.

Practical calculation

In practice, it looks like this:

We will invest 200 thousand rubles on a deposit at 11% of the monthly capitalization of interest. We get that for the first month 11% ÷ 12 = 0.917% should be charged.

Further, 200 thousand rubles * 0.917% = 1834 rubles. In the second month, the deposit amount will increase by 1834 rubles.

That is, in the second month it will be 201834 rubles. And in the same way you can calculate the remaining months:

• 3 months - 201834 * 0.917% = 1850.82. The amount of the deposit will amount to 203684.82 rubles;
• 4 months - 203684.82 * 0.917% = 1867.11. The contribution will be equal to 205551.93 p.;
• 5 months - 205551.93 * 0.917% = 1884.23. The body of the deposit will already be 207436.16 p;
• 6 months - 207436.16 * 0.917% = 1901.50. It turns out that in the 7th month the deposit will be equal to 209337.66 p.

In the same way, you can calculate the remaining six months. The results will be as shown in the following table:

Total, by the last month of the year, the amount of compound interest will amount to 21118.33 rubles, and at the end of the year a person will receive 223126.33 rubles in his hands.If he placed his money on a regular deposit without a monthly capitalization, then the amount of interest would be 22,000 rubles. It turns out that by 1126.33 rubles a contribution with a compound interest was more profitable.

That is, it turns out that it is really profitable to place such deposits. But this is in theory, in practice, perhaps everything will be different due to some nuances that will be described somewhat below.

How to compare compound and simple interest in practice?

In practice, we meet with banks that do not want to work at a loss. According to the calculations made above, deposits with a complex rate are less profitable for any bank.

This can explain the difference in interest rates that financial institutions offer as a reward for deposit placement. Those deposits that involve capitalization always have a lower interest rate.

Deposits without capitalization always have a higher level of offered interest rates.

In order to make a real comparison, we take the average rates that exist today.

Imagine that Ivanov K.L. is the proud owner of 1 million rubles. He decided to place this money in a bank. The bank officer offered him two options. The first is to place a contribution for 1 year at 10% per annum, implying the calculation of compound interest. The second option is a two-year contribution at 11% per annum with simple accrual of fees.

Which option to choose? Let's make a calculation.

Comparison will help to really assess the profitability of a particular offer.

The previous example showed in detail how to calculate interest for each month. This time we’ll do it easier - we will use the already derived compound interest formula, which looks like this:

Ps = D * (1 + Ds / 100 * Pd / Po) K - D, where:

• D - initial deposit amount;
• Ds - interest rate on the deposit;
• PD - the number of days in the period (often 30 calendar days);
• By - the total number of days in the period for which the deposit agreement is concluded;
• K - the number of periods in which interest will be transferred to the body of the deposit.

According to the formula, we calculate what are the compound annual interest in our example:

Ps = 1 000 000 * (1 + 10 * / 100 * 30/365) 12 - 1 000 000 = 103 213.20 rubles.

If Ivanov K.L. if he chooses the second option, he will receive the following amount of interest in a year:

Pn = 1 000 000 * 0.11 = 110 000 p.

As you can see, even a 1% difference significantly affects the level of difference in remuneration for deposits with and without capitalization. Of course, if the interest rate were the same, then capitalization is always more profitable. But the reality is that banks knowingly lower interest rates on such deposits so as not to incur losses.

A deposit is not a way to make money, but an opportunity to preserve the value of equity

Of course, a compound interest on deposits allows their owners to earn more money for the allotted time unit. In the examples above, you can see the difference in the amount of remuneration received.

But you need to consider the rate of inflation, growth or decline of the economy. In the current situation, economists are of the opinion that deposits only help to cope with factors that influence the process of depreciation of money.

Of course, banking institutions provide guarantees to protect your money, and this method is much better than keeping valuables under a mattress, but if you want to create new capital with the help of capital, you need to choose an investment.

If you have already decided exactly what type of account you need, do not make hasty decisions. Even if a deposit with capitalization of interest has a very attractive interest rate, it is worth evaluating all the risks that may arise. The bank's reputation in this matter plays a large role, which indicates the reliability of the institution.

For example, we can say that abroad, all people are alien to deposit interest rates, such as in Russia. In the same way they apply to interest rates on loans.There, their level in the region of 1-2 percent is considered normal. In this regard, they perceive banks exclusively as a means of saving their funds.