Compound interest is the total interest that we get on the principal and interest together over a given period of time. Compound interest is another new method to calculate all the interests used in various financial transactions. In this article, we’ll learn in detail about the compound interest formula and the various calculations that take place using this method.

**What is Compound Interest?**

The interest that is calculated and paid on both the principal amount and the interest, compounded at regular intervals is known as the compound interest. After every regular interval, the new principal is equal to the sum of the original principal and the interest collected till the given time. The regular intervals at which the compound interest is calculated can be annually, semi-annually, quarterly, monthly, etc.

**Compound Interest Formula**

Compound interest is determined after calculating the total amount over a given time period, considering the interest rate and the original principal. The formula for calculating compound amount is,

A = P(1 + r/n)^{nt}

Given that A is used to denote the total accumulated amount after a certain interval, P is the initial principal amount on which the interest is calculated, r is the rate of interest at which the interest is determined, n is the number of times the interest is compounded and lastly, t indicates the given duration for the whole transaction to take place.

From the above formula, we can find out the compound interest. The formula for compound interest is,

CI = P (1 + r/n)^{nt} – P

In the given expression, P is the initial principal amount on which the interest is to be calculated, r is the rate of interest at the principal, n is used to indicate the number of times the interest is compounded annually, and t means the total duration mentioned.

**Difference between Simple Interest and Compound Interest**

- Simple interest is determined on the initially given principal amount every time, whereas compound interest is calculated on the sum of the principal and interest.
- The formula to calculate simple interest is, SI = P×R×T, whereas to calculate compound interest, the formula is, CI = P (1 + r)
^{t}– P. - The simple interest is kept equal for every year on the given principal, whereas compound interest is different for every interval since it is determined considering the compounded amount and not the principal.

**Compound Interest Formula for Different Periods of Time**

**Formula for Half-Yearly:**

When the given time period for the calculation of the interest is half-yearly, then the interest is to be calculated for every six months and the amount is compound twice each year.

When the principal is compounded semi-annually, then the formula to calculate the required compound interest is.

CI = P (1 + 100r/2)^{2t} – P

Since the interest is calculated for a period of half a year, the rate of interest r is divided by 2 and the given period is multiplied by 2, i.e., it is doubled.

**Formula for Quarterly:**

If the given time is said to be quarterly, then the interest is to be calculated for every 3 months and the amount is compounded 4 times a year. The required formula to calculate the compound interest when we have the principal compounded quarterly is,

CI = P (1 + 100r/4)^{4t} – P

Since the interest is calculated for a quarterly period, the rate of interest is divided by 4 and the period is multiplied by 4.

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