Each person who wants to open a bank account has the task of choosing the best bank and the most profitable type of account. And if everything is more or less clear with banks - you can navigate through 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. Indeed, in addition to the percentage, one must also take into account the possibility of replenishing the deposit, early withdrawal, the method of calculating interest and other factors. In addition to the size of the percentage itself, its appearance is of great importance. Let us consider in detail how the simple and compound percentages differ.
Simple percentage. Calculation formula
With a
simple percentage, everything is extremely clear, because it is studied at school. The only thing to remember is that the rate is always indicated for the annual period. The formula itself has the following form:
KS = NS + NS * i * p = NS * (1 + i * p), where
NS - the initial amount
KS - the final amount
i - 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 look at a few examples:
1. A depositor places 50 thousand rubles on a fixed deposit at 6% per annum for 4 months.
COP = 50,000 * (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 on the card (they do not join the deposit).
COP = 80,000 * (1 + 0.12 * 1.5) = 94,400.00 p. (since the quarterly interest payment is not added to the deposit amount, this fact does not affect the final amount)
3. The depositor decided to put 50,000 rubles on a fixed-term deposit, at 8% per annum for 12 months. It is allowed to replenish the deposit and for 91 days a replenishment of the account in the amount of 30,000 rubles was made.
In this case, you need to calculate the interest on two amounts. The first is 50,000 p. and 1 year, and the second 30,000 rubles and 9 months.
KS1 = 50000 * (1 + 0.08 * 12/12) = 54000 p.
KS2 = 30000 * (1 + 0.08 * 9/12) = 31800 p.
KS = KS1 + KS2 = 54000 + 31800 = 85800 p.
Compound interest. Calculation formula
If it is indicated in the terms of deposit placement that capitalization or reinvestment is possible, then this indicates that in this case a compound interest will be used, the calculation of which is carried out according to the following formula:
KS = (1 + i) n * NS
Designations are the same as in the formula for a simple percentage.
It so happens that interest is paid more often than once a year. In this case, the compound percentage is calculated a little differently:
KS = (1 + i / k) nk * NS, where
to - the frequency of savings per year.
Let us return to our example, in which the bank accepted a term deposit of 80 thousand rubles, at 12% per annum for 1.5 years. Suppose that interest is also paid quarterly, but this time they will be added to the body of the deposit. That is, our deposit will be with capitalization.
COP = (1 + 0.12 / 4) 4 * 1.5 * 800000 = 95524.18 p.
As you already managed to notice, the result was 1124.18 rubles more.
Compound interest advantage
A compound percentage compared to a simple one always brings more profit, and this difference increases faster and faster over time. This mechanism is able to turn any start-up capital into a super-profitable machine, you just have to give it enough time. At one time, Albert Einstein called the compound percentage the most powerful force in nature. Compared to other types of investments, this
type of contribution has significant advantages, especially when the investor chooses a long-term period. Compared to stocks, compound interest has a much lower risk, and stable bonds yield less return. Of course, any bank can go broke over time (anything happens), but choosing a banking institution that participates in the state deposit insurance program can reduce this risk to a minimum.
Thus, it can be argued that a compound interest has much greater prospects compared to almost any financial instrument.