What is the compound interest and what is its advantage?

Before each person wishing to open a bank account, the task of selecting the best and most profitable bank account type.And if the banks are more or less clear - it is possible to navigate the numerous ratings and choose the office that is located not far from the place of residence, with a choice of the type of account, the situation is much more complicated.After all, in addition to the rate of interest should be considered another opportunity to replenish the deposit early withdrawal, the method of interest calculation and other factors.In addition to the size of the percentage it is of great importance its kind.Consider in detail what is the difference between a simple and compound interest.

Simple Interest.The formula for calculating

With simple interest, everything is clear, as it is studied in school.The only thing to remember is that the rate is always specified for the year.Directly formula itself has this form:

COP = HC + NA * i * p = NS * (1 + i * n), where

NA - the initial amount

,

COP - finite sum,

i -the interest rate.For the deposit for a period of 9 months and an interest rate of 10%, i = 0,1 * 9/12 = 0.075, or 7,5%,

n - the number of compounding periods.

Consider a few examples:

1. The investor puts 50 thousand. Rubles for the term deposit at 6% per annum for 4 months.

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

2. Term deposit 80 thousand. Rubles under 12% per annum for 1.5 years.This interest is paid quarterly on the card (not connected to the deposit).

COP = 80000 * (1 + 0.12 * 1.5) = 94400.00 p.(as the quarterly payment of interest is not added to the deposit amount, then the final sum this has no influence)

3. The investor decided to put 50,000 rubles for the term deposit at 8% per annum for 12 months.Allowed to replenish the deposit and 91-day refill was made in the amount of 30,000 rubles.

In this case, you need to calculate interest on the two amounts.First - this 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.

CS2 = 30000 * (1 + 0.08 * 9/12) = 31800 p.

COP = KS1 + KS2 = 54000 + 31800 = 85800 p.

compound interest.The formula for calculating

If the conditions of the deposit indicates that the possible capitalization or reinvestment, it says that in this case will be used compound interest, which is calculated by the following formula:

COP = (1 + i) n * NA

designations are the same as in the formula for the simple interest.

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

COP = (1 + i / a) nk * NA where

to - the frequency of savings per year.

Returning to our example, in which the bank adopted a fixed deposit of 80 thousand rubles. At 12% per annum for 1.5 years.Assume also that the interest paid on a quarterly basis, but this time they will be added to the body of the deposit.That is, we will deposit with capitalization.

COP = (1 + 0.12 / 4) 4 * 1.5 * 800,000 = 95,524.18 p.

As you already may have noticed, the result was at 1124.18 rubles more.