Table of Contents

## Introduction

Interest is the amount that is calculated on the principal amount of money at a certain rate of percentage for a specified period as decided by the bank or financial institutions where the money is deposited. The period for which the compound interest is calculated can be annual (yearly), semi-annual, quarterly, or monthly. The commonly used interest can be of two types, namely simple interest and compound interest. The simple interest is calculated based on the original principal amount for every period whereas compound interest takes into consideration the total amount including the interest, for the calculation of interest for next period. So, the compound interest formula calculation is on the accumulated principal value that is higher than the original principal.

## Simple vs Compound interest

Compound interest is the interest paid on both principal and interest and clubbed with the existing principal amount to get a new principal amount on which the interest is calculated for the next period. Compound interest for the first period is the same as simple interest but gives higher returns over time as compared to simple interest. The simple interest amount remains the same for each period but the compound interest increases in every successive period. The final amount including the interest over a longer period is more with compound interest than with simple interest. Banks or any financial organizations provide compound interest rates to encourage customers to deposit money and get more returns.

## Compound Interest Formula

To calculate the compound interest, we have to understand the basic difference between simple interest and compound interest computation. For simple interest, the principal remains constant over time, whereas for compound interest, the interest is added to the principal and the base amount for interest computation increases for every period.

For example, for a principal amount of Rs. 20,000, with a simple interest rate of 5% annually, the interest amount for each year will be 5% of Rs. 10,000 which is Rs. 1000. This amount is the same for each consecutive year, so Rs. 1000 will be the interest accumulated each year on the principal amount of Rs. 20,000.

For compound interest calculation, after calculating the interest amount as Rs. 1000 in the first year, the same is clubbed with the principal for the calculation of interest in the second year. Therefore, the principal for the second year becomes Rs. 21,000 on which interest will be calculated at 5% which will be Rs. 1050. This is again added to the principal Rs. 21.000 and the new principal for the next year will be Rs. 22.050. This method is applied for each period.

The formula used for compound interest A = P(1 + r/100) raised to the power n.

Here P is the principal, r is the interest rate, n is the period for which the interest is compounded.

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