Cuemath is an online teaching platform that helps students develop their ability to analyze and solve complex mathematical problems. The math program is designed to provide conceptual learning by introducing the concept of math through different fun activities and multiple pictorial models. All mathematical concepts are covered by Cuemath in their curriculum. Through this article, you can learn more about the compound interest formula.

## What is the meaning of compound interest?

Compound interest is the interest that is calculated on both the principal and the interest accrued on the principal for a given period. Here, the interest is added to the given amount of money (principal) when the interest for the next period is calculated. It is used to calculate the increase or decrease in the population of an area, the appreciation or depreciation of the value of an item, the growth of bacteria, etc.

Compound interest = Interest on principal + Compound interest at regular time intervals

## What is the formula for calculating compound interest?

To calculate compound interest, we will first need to calculate the total amount over a given period, based on the initial principal and the given interest rate. The amount is calculated using the following mathematical formula:

Amount (A) = P (1 + r / 100) t

Using the above formula, the total amount at the end of the period is calculated, which also includes compound interest and principal. Now, after calculating the total amount, the compound interest can be calculated by subtracting the principal from the total amount calculated.

## Before knowing the compound interest formula, you should know the following terms:

__Principal (P)__: It is the sum of money that is loaned for a fixed period at a certain interest rate.__Time____Interest rate (r)__: It involves the percentage of interest that is earned by lending the principal.__Interest (I)__: it is the amount of profit that is made by lending a sum of money for a given period.__Compound interest (CI)__: This is the total amount of annual interest that is charged on the loan of a sum of money for a given period.__Amount (A)__: The amount is the sum of the initial principal and the total amount of compound interest earned.

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

Compound Interest (CI) = A – P

= P [(1 + r/100) t – 1]

Or,

P = Principal

r = interest rate

n = frequency of the number of times interest is compounded per year

t = time (in years)

The above formula is generally used to calculate compound interest when a given amount of money (principal) is compounded n number of times in a given year.

## How to calculate semi-annual and quarterly compound interest?

__Semi-annual compound interest__:

At the time that interest is accrued semi-annually, then, at that time, the leader’s measure changes towards the end of the initial semester, and interest for the following semester is determined on the full amount after the first six months. In short, to calculate compound interest, the rate is divided by 2, and the time is multiplied by 2.

__Interest compounded quarterly__:

When interest is compounded quarterly, the principal changes at the end of the first three months. Interest for the next three months is calculated on the amount remaining after three months. Third quarter interest is calculated on the six month amount and fourth quarter interest is calculated on the nine month amount. In short, to calculate compound interest, the rate is divided by 4, and the time is multiplied by 4.

There are several applications of compound interest in real life. As we have discussed the basic concept of compound interest, if you have any doubts about the concept of simple interest, you can seek Cuemath’s help and dispel all your doubts.