Step 1: Calculate Simple Interest and Amount

First, calculate the simple interest earned over the initial 2 years and determine the total amount accumulated.

• Principal (P) = ₹1,000
• Interest Rate (R) = 5% per annum
• Time (T) = 2 years

The formula for Simple Interest (SI) is:

\(SI = \frac{P \times R \times T}{100}\)

Substituting the values:

\(SI = \frac{1000 \times 5 \times 2}{100} = ₹100\)

The total amount (A) after 2 years is the sum of the principal and the simple interest:

\(A = P + SI = 1000 + 100 = ₹1100\)

Step 2: Calculate Compound Interest on the Initial Simple Interest

The question asks for the 'average interest earned'. Based on the calculation and options, this refers specifically to the compound interest earned on the initial simple interest amount (₹100) over the 4-year period.

• Principal for CI (P_CI) = ₹100 (This is the SI calculated in Step 1)
• Interest Rate (R) = 5% per annum
• Time (T_CI) = 4 years

The formula for the Amount (A_CI) using compound interest is:

\(A_{CI} = P_{CI} \times \left(1 + \frac{R}{100}\right)^{T_{CI}}\)

Substituting the values:

\(A_{CI} = 100 \times \left(1 + \frac{5}{100}\right)^4\)

\(A_{CI} = 100 \times (1.05)^4\)

\(A_{CI} = 100 \times 1.21550625\)

\(A_{CI} = ₹121.550625\)

Step 3: Determine the Average Interest Earned

The required value is the compound interest earned on the ₹100 principal over 4 years.

The formula for Compound Interest (CI) is:

\(CI = A_{CI} - P_{CI}\)

Calculation:

\(CI = 121.550625 - 100 = ₹21.550625\)

Rounding to two decimal places, the average interest earned is ₹21.55.