Compound Interest: Explanation, Formula and Example

|Updated on: January 13, 2020

What is Compound Interest?

We all have learnt the principles of calculating Compound Interest while we were in school. But, with so many other things which take our priority in life, it’s nearly impossible to remember everything that you learnt in school, right? So, here’s a refresher about this simple yet crucial concept of calculating the interest amount will help manage your accounts more seamlessly.

Compound interest is when interest is earned not only on the initial amount invested, but also on any interest. In other words, interest is earned on top of interest and thus “compounds”. The compound interest formula can be used to calculate the value of such an investment after a given amount of time, or to calculate things like the doubling time of an investment.

Formula to Calculate Compound Interest

Compound interest is calculated based on the principal, interest rate (APR or annual percentage rate), and the time involved:

P is the principal (the initial amount you borrow or deposit)

r is the annual rate of interest (percentage)

n is the number of years the amount is deposited or borrowed for.

A is the amount of money accumulated after n years, including interest.

When the interest is compounded once a year:

A = P(1 + r)n

However, if you borrow for 5 years the formula will look like:

A = P(1 + r)5

This formula applies to both money invested and money borrowed.

Example to Understand Calculation of Compound Interest

Let’s look at an example to understand Compound Interest in a better way.

Ritu made an investment of Rs 50,000, with an annual interest rate of 10% for a time frame of five years. With compound interest calculated on it, the interest for the initial year will be calculated on the below mentioned basis: 50,000 x 10/100 = Rs. 5,000

Similarly, the interest for Ritu’s second year will be calculated on the accumulated amount, i.e: 50,000 + 5000 = 55,000. Hence, the interest for the second year will be calculated on this basis: 55,000 (which is 50,000 plus 5,000) x 10/100 = Rs. 5,550

Similarly, the interest for the third year will be calculated on this basis: 50,000+5,000+5,550 = Rs. 60,550*10/100 = Rs. 6055.

Moving forward with a similar calculation, the interest for the fourth year for Ritu’s initial investment of Rs 50,000 will be calculated on this basis:

50,000+5,000+5,550+6055 = Rs. 66,605 *10/100 = 6,660.5

The final interest for the fifth year will be

50,000+5,000+5,550+6055+6,660.5 = Rs. 73265.5*10/100 = Rs. 7,326.55

Thus, we see that with the power of compounding, Ritu has earned a substantial interest of

5,000 + 5,550 + 6055 + 6,660 + 7,326.55= Rs 30,591.55

Hence, Ritu’s total investment after a period of five years has amounted to

Rs 50,000 + Rs 30,591.55 = Rs 80,591.55

The compound interest formula is used when an investment earns interest on the principal and the previously-earned interest. Investments like this grow quickly; how quickly depends on the rate and the number of compounding periods. When working with a compound interest formula question, always make note of what values are known and what values need to be found so that you stay organized with your work.

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