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

## What is the meaning of compound interest?

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

Compound Interest = Interest on Principal + Compounded Interest at the regular time interval

## What is the formula to calculate Compound Interest?

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

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

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

## Before knowing the formula of calculating compound interest you should be aware of the following terms:

__Principal (P)__: It is the sum of money that is lent for a specific period at a certain rate of interest.__Time (t)__: It is the period for which the principal is lent. Most time is taken in the years.__Rate of interest (r)__: It implies the percentage of interest which is earned by lending the principal.__Interest (I)__: it is the amount of profit that is earned by lending a sum of money for a given period.__Compound Interest (C.I)__: It is the total amount of annual interest which is earned on lending a sum of money for a given period.__Amount (A)__: Amount is the sum of initial principal and the total amount of compound interest earned.

## The mathematical formula to calculate compound interest is as follows:

Compound Interest (C.I) = A – P

= P [(1 + r/100) t – 1]

Where,

P = Principal

r = rate of interest

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

t = time (in years)

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

## How to calculate half-yearly and quarterly compound interest?

__Interest compounded half-yearly__:

At the point when the interest is accumulated half-yearly, then, at that point, the measure of chief changes toward the finish of the initial a half year, and the interest for the following a half year is determined on the total amount after the first six months. In short, to calculate compound interest, the rate is divided by 2, and time is multiplied by 2.

__Interest compounded quarterly__:

When the interest is compounded quarterly, then the principal changes at the end of the first three months. The interest for the next three months is calculated on the amount remaining after three months. The interest for the third quarter is calculated on the amount after six months and interest for the fourth quarter is calculated on the amount of nine months. In short, to calculate compound interest, the rate is divided by 4, and 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 doubt related to the concept of simple interest then you can take the help of Cuemath and can clear all your doubts.

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