Simple Interest Calculation Explained

This solution explains how to calculate the simple interest on a given principal amount over a specific period at a certain interest rate.

Understanding Simple Interest

Simple interest is a straightforward method for calculating the interest charged on a loan or earned from an investment. The interest is calculated solely based on the initial amount, which is called the principal. It does not include the effect of compounding.

Key Information Provided

• Principal Amount (P): ₹1,280
• Annual Interest Rate (R): 5% per annum (p.a.)
• Time Period (T): 3 years

The Simple Interest Formula

To calculate the simple interest (SI), we use the following standard formula:

Where:

• \(P\) is the Principal amount
• \(R\) is the Rate of interest per year
• \(T\) is the Time period in years

Step-by-Step Calculation

1. Identify the values:
   From the question, we have:
   \(P = 1280\)
   \(R = 5\) (since the rate is 5%)
   \(T = 3\)
2. Substitute the values into the formula:
   Plug these values into the simple interest formula:
   
   \(SI = \frac{1280 \times 5 \times 3}{100}\)
3. Calculate the product in the numerator:
   First, multiply the principal, rate, and time:
   \(1280 \times 5 = 6400\)
   \(6400 \times 3 = 19200\)
   So, the numerator is \(19200\).
4. Divide by 100:
   Now, divide the result by 100:
   
   \(SI = \frac{19200}{100}\)
5. Determine the final Simple Interest:
   Performing the division gives the simple interest:
   \(SI = 192\)

Conclusion

The calculation shows that the simple interest on ₹1,280 at an annual interest rate of 5% for a time period of 3 years is ₹192.