To determine the principal sum (P), we need to use the concept of compound interest. Given that the interest earned during the 2^nd year is ₹3,342 and the rate of interest is 20% per annum compounded annually, we can find the sum effectively using the formula for compound interest.

Compound interest is calculated as: A = P(1 + \frac{r}{100})^n, where:

• A is the amount after n years,
• P is the principal amount,
• r is the rate of interest per annum,
• n is the number of years.

For the second year interest, the formula is:

• Interest for 2^nd year = A_2 - A_1
• Using the principle for the 1^st year, A_1 = P(1 + \frac{r}{100})
• For 2^nd year, A_2 = A_1(1 + \frac{r}{100}) = P(1 + \frac{r}{100})^2

The interest in the 2^nd year is given by:

• A_2 - A_1 = P(1 + \frac{r}{100})^2 - P(1 + \frac{r}{100})
• Simplifying: P\left((1 + \frac{r}{100})^2 - (1 + \frac{r}{100})\right) = ₹3,342

Substitute r = 20:

• Year values: (1 + \frac{20}{100}) = \frac{6}{5}
• (1 + \frac{20}{100})^2 = \left(\frac{6}{5}\right)^2 = \frac{36}{25}

The interest is calculated as:

• P\left(\frac{36}{25} - \frac{6}{5}\right) = ₹3,342
• Simplifying: P\left(\frac{36 - 30}{25}\right) = ₹3,342
• P\left(\frac{6}{25}\right) = ₹3,342

Solve for P:

• P = \frac{3,342 \times 25}{6}
• P = ₹13,925

Thus, the principal sum is ₹13,925, which corresponds to the correct answer.