Effective Annual Rate – 5% nominal compounded half-yearly: Find the effective annual rate corresponding to a nominal 5% per annum when interest is compounded half-yearly.

Introduction / Context:
Converting nominal rates with intra-year compounding to an effective annual rate (EAR) is essential for fair comparisons. Half-yearly compounding at a 5% nominal rate produces a slightly higher true annual yield than 5% due to two compounding steps per year.

Given Data / Assumptions:

• Nominal r = 5% per annum
• Compounding frequency m = 2 (half-yearly)
• EAR formula: (1 + r/m)^m − 1

Concept / Approach:
Compute per-period rate r/m = 0.05/2 = 0.025, then square (1.025) to obtain the one-year growth factor and subtract 1 to find the EAR in percent.

Step-by-Step Solution:
Per half-year factor = 1.025Annual growth factor = (1.025)^2 = 1.050625EAR = 1.050625 − 1 = 0.050625 = 5.0625%

Verification / Alternative check:
Expressed in percent, 0.050625 → 5.0625%. This is a classic value that often appears in exams for nominal 5% with semiannual compounding.

Why Other Options Are Wrong:
1.025% interprets the per-period rate incorrectly as an EAR; 5.062% is rounded; 5.500% and “None of these” are not the exact effective rate.

Common Pitfalls:
Using 5% directly as EAR ignores compounding; multiplying 2.5% by 2 without exponentiation also gives the wrong result. Always exponentiate across periods to get EAR.

Final Answer:
6.0625%