Compound interest is a method of calculating the total amount of income that has been generated after a given period of time at a specified rate of interest plus the principle amount of money that was granted as loan. The concept of compound interest has found its application in various fields like banking sector, money lending and borrowing, housing finance sector, mortgaging etc.

At all these places, the concept of compound interest have proved to be of a great use and the dependence of the modern day finance sector is, therefore intensely dependent on calculating the compounded interest on the money that is being deposited or is being taken as loans.

Hence, compound interest is taken as a standard method to calculate the resulting amount of money. Now let’s get a glimpse of the compound interest formula and have a thorough insight on how it works.

## Compound interest

P’= P (1+ r/n)nt

This is the standard formula for calculating compound interest. In this formula, the standard notations have been used.

### The standard meanings of these notations are as follows:

• P’ denotes the total amount that will be returned after the given period of time.
• P denotes the principle amount that was granted as a loan.
• r denotes the rate of interest that has been specified by the money lender or the bank.
• n denotes the number of times that the interest has been compounded per year.
• t denotes the number of years after which the money is guaranteed by the borrower to be returned.

It is important to note that in this formula, the value of P’ is the total amount of money that will be returned, that means that the amount will be the sum of the principle amount and the interest that is compounded for that principle amount at the given rate and for the specific period of time.

There is also a formula for calculating only the total interest that has been generated. This formula has been derived from the original formula for compound interest; the only difference is the subtraction of the principle amount P from the total amount P’.

I=P’–P

I= P (1+ r/n)nt –P

In this formula, the meaning of every notation is same as the meanings given above. The only unknown symbol is I which denotes the amount generated as the interest.

## Method to calculate

To understand the working of these formulas, we need to take up some examples to illustrate the proper way to apply these formulas to get the perfect results.

Let’s suppose the principle amount that is to be provided as a loan is \$2,000. The loan is to be given for duration of 3 years at a rate of 4%. The interest will be compounded quarterly. The compound interest and the total amount can be calculated as follows.

Studying the above given data carefully we can draw some basic details like:

P= \$2,000

r= 4%= .04

n= 4

t= 3

Now take these values and values and applying it to the formula for total amount, we will get an equation similar to

P’= 2000*(1+ 0.04/4)4*3

P’= \$2,253.65

Therefore, the total amount that the money lender will be taking from the one who borrowed \$2,000 from him will be equivalent to \$2,253.65 and the total amount of interest that has been generated from this will be the difference of \$2,253.65 and \$2,000, which is equal to \$253.65. Hence, this is how to calculate compound interest.