Explanation:

Given information for a simple interest calculation:\nPrincipal amount ($P$) = $₹12,500$.\nAmount ($A$) after $4$ years = $₹15,500$.\nTime ($T$) = $4$ years. \nFirst, calculate the Simple Interest (SI) earned over $4$ years: $\text{SI} = A - P$ $\text{SI} = ₹15,500 - ₹12,500 = ₹3,000$. \nThe formula for Simple Interest is: $\text{SI} = \frac{P \times R \times T}{100}$\nWhere $R$ is the annual rate of interest in percentage. \nWe need to find $R$. Rearranging the formula to solve for $R$: $R = \frac{\text{SI} \times 100}{P \times T}$ \nSubstitute the known values into the formula: $R = \frac{3000 \times 100}{12500 \times 4}$ $R = \frac{300000}{50000}$ \nSimplify the expression: $R = \frac{300}{50}$ $R = 6$. \nSo, the rate of interest is $6\%$. \nLet's evaluate the options:\nOption (1) $4\%$: If $R=4\%$, $\text{SI} = \frac{12500 \times 4 \times 4}{100} = 125 \times 16 = ₹2000$. This is not $₹3000$.\nOption (2) $6\%$: This matches our calculated rate. If $R=6\%$, $\text{SI} = \frac{12500 \times 6 \times 4}{100} = 125 \times 24 = ₹3000$. This is correct.\nOption (3) $8\%$: If $R=8\%$, $\text{SI} = \frac{12500 \times 8 \times 4}{100} = 125 \times 32 = ₹4000$. This is not $₹3000$.\nOption (4) $2\%$: If $R=2\%$, $\text{SI} = \frac{12500 \times 2 \times 4}{100} = 125 \times 8 = ₹1000$. This is not $₹3000$. \nTherefore, the rate of interest is $6\%$. The correct option is (2) 6%.