Comparing compound interest rates (Half-yearly vs Annually)

Write out the compound interest equations for a 1-year timeline under both scenarios[cite: 3744, 3745]:

Q = P \left(1 + R/200\right)²

Q = P \left(1 + S/100\right)^1

Since the final amount Q and initial principal P are identical in both cases, equate the multipliers [cite: 3744, 3745]: \left(1 + R/200\right)² = 1 + S/100 1 + R/100 + R²/40000 = 1 + S/100 R/100 + R²/40000 = S/100

Because the term ⟨MATH⟩R²/40000⟨/MATH⟩ is strictly positive, it follows that ⟨MATH⟩S/100⟨/MATH⟩ must be strictly greater than ⟨MATH⟩R/100⟨/MATH⟩. This forces S > R, which can be rewritten as R < S.

Answer: (c).