Calculating Compound Interest Explained

This problem asks us to find the compound interest on a principal amount when the interest is compounded annually. Let's break down the steps to solve this compound interest problem.

Understanding Compound Interest

Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods. It's often described as "interest on interest," and it makes a sum grow at a faster rate than simple interest.

Given Information

From the question, we are given the following details:

• Principal amount (P) = Rs. 8000
• Rate of interest (R) = 15% per annum
• Time period (n) = 2 years
• Compounding frequency = Annually

Formula for Compound Interest Calculation

To find the compound interest (CI), we first need to calculate the total amount (A) after the given period. The formula for the amount when interest is compounded annually is:

\( A = P \left(1 + \frac{R}{100}\right)^n \)

Where:

• \( A \) is the amount after \( n \) years
• \( P \) is the principal amount
• \( R \) is the annual interest rate in percent
• \( n \) is the number of years

Once the amount \( A \) is calculated, the compound interest (CI) is found using the formula:

\( \text{CI} = A - P \)

Step-by-Step Calculation of Compound Interest

Let's substitute the given values into the formula for the amount:

\( A = 8000 \left(1 + \frac{15}{100}\right)^2 \)

First, simplify the term inside the bracket:

\( 1 + \frac{15}{100} = 1 + 0.15 = 1.15 \)

Now, substitute this back into the formula for A:

\( A = 8000 (1.15)^2 \)

Calculate \( (1.15)^2 \):

\( (1.15)^2 = 1.15 \times 1.15 = 1.3225 \)

Now, calculate the amount A:

\( A = 8000 \times 1.3225 \)

\( A = 10580 \)

So, the total amount after 2 years is Rs. 10580.

Now, calculate the compound interest (CI):

\( \text{CI} = A - P \)

\( \text{CI} = 10580 - 8000 \)

\( \text{CI} = 2580 \)

Therefore, the compound interest on Rs. 8000 at 15% per annum for 2 years, compounded annually, is Rs. 2580.

Calculation Summary Table

Checking the Options

Let's compare our calculated compound interest with the given options:

• Rs. 2450
• Rs. 2580
• Rs. 2400
• Rs. 2550

Our calculated compound interest is Rs. 2580, which matches one of the options.

Revision Table: Compound Interest Concepts

Additional Information: Compound Interest vs Simple Interest

It is helpful to understand the difference between compound interest and simple interest.

• Simple Interest: Interest is calculated only on the initial principal amount for the entire duration. The interest earned in each period does not get added to the principal for calculating interest in the next period. Formula: \( \text{SI} = \frac{P \times R \times n}{100} \).
• Compound Interest: Interest is calculated on the principal plus any accumulated interest from previous periods. The interest earned in each period is added to the principal, and the next period's interest is calculated on this new, larger principal. This leads to exponential growth.

In this problem, if it were simple interest, the calculation would be:

\( \text{SI} = \frac{8000 \times 15 \times 2}{100} = \frac{240000}{100} = 2400 \)

The simple interest would be Rs. 2400, which is less than the compound interest (Rs. 2580), illustrating how compounding earns more over time.