Class 8 - Compound Interest

Compound Interest is when you have deposited some money in a bank. Every year, some interest is added to it. The interest is not the same every year, but it goes on increasing year after year. This is because, at the end of the first year, simple interest is calculated and added to the principal to get the amount. This amount becomes the principal for the next year. At the end of the second year again, the amount is found by adding the principal and the interest. This amount becomes the principal for the third year and so on. Each year, the principal changes. Interest is calculated on the amount of the previous year. When interest is calculated in this manner, we call it compound interest. Financial institutions generally do not calculate simple interest. They calculate the interest periodically.

First, they add the interest for one time period to the principal and use it as the principal for the next time period.

Table of Content

• What is Compound Interest?
• Compound Interest Formula
• Solved Examples on Compound Interest
• Practice Problems on Compound Interest

What is Compound Interest?

Compound Interest (CI) is the interest calculated on the initial principal and also on the accumulated interest from previous periods. In other words, at the end of each compounding period usually one year, the interest earned is added to the principal, and the next period's interest is calculated on this new, larger principal. This process of earning interest on interest is called "compounding."

Also use: Compound Interest Calculator

Compound Interest Formula

Consider that P is the principal amount, T = n is the time period, R is the rate of interest per annum.

Then, the amount after n yearsA=P(1+R100)n

Compound InterestCI=A−P

Let:

• P be the principal amount

• T (or n) be the time period (in years)

• R be the rate of interest per annum

Note: The interest is compounded annually.

The difference between interest and compound interest is given below.

Basis	Simple Interest (SI)	Compound Interest (CI)
Definition	Interest calculated only on the principal amount.	Interest calculated on principal + accumulated interest.
Formula	PRT100	A=P(1+R100)n
Interest Calculation	Same every year	Changes every year
Growth Type	Linear growth	Exponential growth
Amount Formula	A=P+SI	A=P(1+R100)n
Usage	Used in short-term loans	Used in investments, banking, and finance