Compound interest is the most frequently encountered concept in our daily lives. If we examine our bank statements, we will notice that some interest is credited to our account each year. For the same principal amount, the interest rate varies from year to year. We can see that interest grows with each passing year. As a result, we can conclude that the interest charged by the bank is not simple interest; rather, it is compound interest, abbreviated as CI. This article will explain what CI is, as well as the formula and derivation of the formula for calculating the CI when compounded annually, half-yearly, quarterly, and so on.

Also, through the examples based on real-life CI applications, one can understand why the return on compound interest is greater than the return on simple interest.

**What is Compound Interest?**

The other name for Compound interest is compounding interest calculated on a loan or deposit based on both the initial principal and the interest accumulated in previous periods. Compound interest, which is thought to have originated in 17th-century Italy, is “interest on interest” and causes a sum to grow at a faster rate than simple interest, which is calculated only on the principal amount.

It is calculated at a rate determined by the frequency of compounding, the greater the number of compounding periods, the greater the compound interest.

Therefore, over the same time period, the amount of compound interest earned on $100 compounded at 10% annually will be less than the amount earned on $100 compounded at 5% semi-annually. Because the interest-on-interest effect can generate increasingly positive returns based on the initial principal amount, compounding is sometimes referred to as the “miracle of compound interest.”

**Compound Interest Formula**

Letâ€™s go through the formula of compound interest –

Compound Interest = P(1+R/100)t-P

Where,

P = Principal

R = Rate

T = Time period

**Compound Interest Example**

A sum of Rs. 10,000 is borrowed and the rate of interest is 5% per annum. What will be the compound interest for a period of 3 years?

**Solution:**

From the formula for compound interest, we know that,

Compound Interest = P(1+R/100)t-P

Here, P = 10,000 ; R = 5% ; T = 3 years ; C.I=?

So, Compound Interest will be-

C.I. = 10000(1+5/100)3-10000

So, compound interest will be Rs. 1576.25, after 3 years at a 5% annual interest rate.

**Applications of Compound Interest**

The compound interest formula’s applications are its mathematical applications in solving real-life problems. The compound interest formula has several applications, which are listed below:

1. Compound interest is not calculated annually (monthly)

2. Population growth and decline

3. Commodity price increases and decreases

4. The item’s value increases and decreases

5. Profit and loss inflation is a term used to describe an increase in profit and loss

6. Transactions at the bank

**Points You Need To Remember**

1. Compound interest (also known as compounding interest) is interest calculated on a deposit or loan’s initial principal plus all accumulated interest from previous periods.

2. Compound interest can be calculated by multiplying the initial principal amount by one and then multiplying the annual interest rate by the number of compound periods multiplied by one.

3. Compounding interest can occur at any time, from continuously to daily to annually.

4. While calculating compound interest, the number of compounding periods makes a significant difference.

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