Principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. Principal = P, Amount = Q, Rate = R%, Time = 1 year $Q = P [1 + R/(2\times100)]^2$ $Q/P = [1 + R/(2\times100)]^2$ …………. (1)

Principal P becomes Q in 1 year when compounded annually with S% annual rate of interest. $Q = P [1 + S/(100)]^1$ $Q/P = [1 + S/(100)]^1$ …………. (2)

From equation (1) and equation (2), we get: $[1 + R/(2\times100)]^2 = [1 + S/(100)]^1$ …………. (3)

Let R = 20%. Putting the value of R = 20 in equation (3), we get: $[1 + 20/(2\times100)]^2 = [1 + S/(100)]^1$ Or 1.21 = 1 + (S/100) Or S/100 = 1.21 – 1 = 0.21 Or S = 0.21 × 100 = 21% Thus, S > R.

Hence, option (C) is correct.