Compound interest (compound or compound interest) is a percentage calculated on the amount of initial capital, which also includes all accumulated interest from previous periods of deposits or loans.

It is believed that this concept originates from 17th-century Italy and can be treated as ‘interest on interest’. Compound interest causes the sum to grow faster than simple interest, which is calculated only on the principal amount.

## Key Facts

- compound interest (or compound interest) is interest accrued on the initial amount of capital, which also includes all accumulated interest from previous periods of the deposit or loan.
- compound interest is calculated by multiplying the initial amount of capital by 1 plus the annual interest rate raised to the power of the number of folding periods minus 1.
- Interest can be calculated according to any frequency schedule – from continuous to daily or yearly.
- When calculating the compound interest, the number of submission periods makes a significant difference.

The level at which compound interest is accrued depends on the frequency of submission, in such a way that the higher the number of compound periods, the greater the amount of compound interest. Therefore, the amount of compound interest accrued from PLN 100 added at 10% per annum will be lower than the amount of PLN 100 added at 5% half-yearly in the same period. Due to the fact that the interest effect can generate more and more profits based on the initial amount of capital, it is sometimes referred to as the “miracle percentage”.

## Calculation of compound interest

The compound interest is calculated by multiplying the initial amount of capital by 1 plus the annual interest rate raised to the power of the number of folding periods minus 1. The total initial loan amount is then subtracted from the final value.

### The formula for calculating the compound interest is as follows:

Compound interest = total capital plus future interest (future value) less the amount of capital currently (current value).

= [P (1 + i)^n] – P = P [(1 + i)^n – 1]

(where P = capital, i = nominal annual interest rate and n = number of periods submitted).

Let’s take a three-year loan of PLN 10,000 at an interest rate of 5%, which accrues annually. What would be the interest amount? In this case, it would be: PLN 10,000 [(1 + 0,05) 3 – 1] = PLN 10,000 [1,157625 – 1] = PLN 1,576.25.

### Increase of compound interest

In the above example, compound interest also includes interest accumulated in previous periods, therefore the amount of interest is not the same for all three years as for simple interest. While the total amount of interest payable over the three-year period of this loan is PLN 1,576.25, interest payable at the end of each year is presented in the table below.