What is a compound interest and what is its advantage?

Before every person who wants to open a bank account, the task is to choose the best bank and the most profitable type of account. And if it's more or less clear with the banks, you can sort by the numerous ratings and choose the branch that is not far from the place of residence, then the choice of the type of account is much more complicated. After all, in addition to the interest, you also need to take into account the possibility of replenishing the deposit, early withdrawal, the way of calculating interest and other factors. In addition to the size of the percent itself, its kind is of great importance. Let's consider in detail, than the simple and compound percent differ among themselves.

A simple percentage. Calculation formula

With a simple percentage of everything is clear, because it is studied in school. The only thing to remember is that the rate is always indicated for the annual period. The formula itself has the following form:

CS = HC + HC * i * n = HC * (1 + i * n), where

НС - the initial sum,

KS is the final sum,

I is the interest rate. For a deposit for a period of 9 months and a rate of 10%, i = 0.1 * 9/12 = 0.075 or 7.5%,

N is the number of accrual periods.

Let's consider some examples:

1. The depositor places 50 thousand rubles on a term deposit, at 6% per annum for 4 months.

KS = 50000 * (1 + 0.06 * 4/12) = 51000.00 p.

2. Term deposit 80 thousand rubles, at 12% per annum for 1.5 years. In this case, interest is paid quarterly to the card (they are not attached to the deposit).

KC = 80000 * (1 + 0.12 * 1.5) = 94400.00 p. (Since the quarterly interest payment is not added to the deposit amount, this circumstance does not affect the final amount)

3. The investor decided to put 50,000 rubles for a term deposit, at 8% per annum for 12 months. Replenishment of the deposit is allowed and on the 91st day the account was replenished in the amount of 30,000 rubles.

In this case, you need to calculate the interest on two amounts. The first is 50,000 r. And 1 year, and the second 30000 rubles and 9 months.

KS1 = 50000 * (1 + 0.08 * 12/12) = 54000 rubles.

KS2 = 30000 * (1 + 0.08 * 9/12) = 31800 rubles.

KS = KC1 + KS2 = 54,000 + 31800 = 85800 rubles.

Difficult percentage. Calculation formula

If in the conditions of deposit placement it is indicated that capitalization or reinvestment is possible, it means that in this case a compound interest will be used, calculated according to the following formula:

CS = (1 + i) ⁿ * HC

The notation is the same as in the formula for prime interest.

It happens that interest is paid more often than once a year. In this case, the compound interest is calculated slightly differently:

CS = (1 + i / k) ^nk * HC, where

K - frequency of savings per year.

Let's return to our example, in which the bank accepted a term deposit of 80 thousand rubles, at 12% per annum for 1.5 years. Assume that interest is also paid quarterly, but this time they will be added to the deposit body. That is, our deposit will be capitalized.

KC = (1 + 0.12 / 4) ^{4 * 1.5} * 800000 = 95524.18 p.

As you have already managed to notice, the result was 1124.18 rubles more.

Advantage of compound interest

Compound interest in comparison with simple always brings more profit, and this difference increases with time faster and faster. This mechanism is able to turn any start-up capital into a super-profitable machine, it is only necessary to give him sufficient time. At one time, Albert Einstein called compound interest the most powerful force in nature. Compared to other types of investments, this kind of contribution has significant advantages, especially when the investor chooses a long-term period. Compared to equities, a compound interest has a much lower risk, and stable bonds yield less revenue. Of course, any bank may eventually go bankrupt (everything happens), but choosing a banking institution that participates in the state deposit insurance program can minimize this risk.

Thus, it can be argued that a compound interest has much greater prospects than almost any financial instrument.