Simple Interest Rate Calculation Explained

This problem involves calculating the rate of simple interest given the principal amount, time period, and the total interest earned.

Understanding the Variables

• Principal Amount (P): The initial amount borrowed, which is Rs. 10000.
• Time Period (T): The duration for which the money was borrowed, which is 4 years.
• Interest Earned (SI): The problem states that Sachin received Rs. 5000 more than the amount given. The amount given was the principal (Rs. 10000). So, the extra amount received by Sachin represents the simple interest. Therefore, SI = Rs. 5000.
• Rate of Interest (R): This is what we need to find.

Simple Interest Formula

The formula to calculate Simple Interest is:

$\text{SI} = \frac{\text{P} \times \text{T} \times \text{R}}{100}$

Step-by-Step Calculation

1. Substitute the known values into the formula:

   $5000 = \frac{10000 \times 4 \times \text{R}}{100}$

2. Simplify the equation:

   First, simplify the fraction part $\frac{10000}{100}$:

   $5000 = 100 \times 4 \times \text{R}$

3. Continue simplifying:

   Multiply 100 by 4:

   $5000 = 400 \times \text{R}$

4. Solve for R:

   To find R, divide both sides of the equation by 400:

   $\text{R} = \frac{5000}{400}$

5. Calculate the final value:

   Simplify the fraction $\frac{5000}{400}$:

   $\text{R} = \frac{50}{4}$

   $\text{R} = 12.5$

   Since R represents the rate of interest, the unit is percent.

   $\text{R} = 12.5\%$

Conclusion

The calculated rate of interest is 12.5%. Comparing this with the given options, Option 1 matches our result.