A sum of Rs. 2000 is lent out at 10% per annum simple interest. What is the difference between the interest earned in the 6th year and the 7th year?

To find the difference between the interest earned in the 6th year and the 7th year for a sum of Rs. 2000 lent out at 10% per annum simple interest, follow these steps:

1. Understand Simple Interest Formula: Simple Interest (SI) = Principal (P) × Rate (R) × Time (T) / 100

2. Identify the Given Values:

   • Principal (P) = Rs. 2000
   • Rate (R) = 10% per annum
   • Time (T) = 1 year (since we are comparing interest earned in individual years)

3. Calculate the Interest for One Year: Using the simple interest formula: $SI = \frac{P \times R \times T}{100}$ Substitute the given values: $SI = \frac{2000 \times 10 \times 1}{100} = \frac{20000}{100} = Rs. 200$

4. Interest Earned in the 6th Year: Since the interest is the same every year in simple interest, the interest earned in the 6th year is Rs. 200.

5. Interest Earned in the 7th Year: Similarly, the interest earned in the 7th year is also Rs. 200.

6. Calculate the Difference: The difference between the interest earned in the 6th year and the 7th year is: $\text{Difference} = \text{Interest in 7th year} - \text{Interest in 6th year} = Rs. 200 - Rs. 200 = Rs. 0$

Therefore, the difference between the interest earned in the 6th year and the 7th year is Rs. 0.