Compound interest arises when interest is added to the principal, and therefore interest also generates interest. That is, we have a multiplier effect of money.
Compound Interest Example
Let’s start with an example, which makes everything simpler. If we have $1000 in an account that gives us 10% interest paid annually, how much money is there after two years? Some will say that $1200, since the first year we will have 100 of interest (10% of 1000), and the second also 100.
However, if interest is deposited in the same account, this is not true, since at the beginning of the second year we will have 1100 euros, and 10% of that amount is 110 euros. So after two years we will have 1210 euros. Therein lies the compound interest.
Calculation of compound interest
In the example below, if C is the initial capital, and the interest rate and we assume that the interest is paid monthly we will have the following capital as the months pass (C1, C2, …):
C1 = C * (1 + i) C2 = C1 * (1 + i) = C * (1 + i) 1 + i) n
Applying this formula to the previous example (you have to change months for years, since the interest is paid annually) we have that the capital after two years would be:
C2 = 1000 * (1 + 0.1) ^ 2 = 1000 * 1.1 ^ 2 = 1000 * 1.21 = 1210 euros
It is important not simply to compare interest rates when comparing financial products, but also pay periods. The law helps us in this regard, since APR, annual equivalent rate, precisely compares interests under similar conditions.