Find the effective annual rate corresponding to a nominal 6% per annum payable half-yearly.

Problem restatementConvert a nominal 6% p.a. with semi-annual compounding into an effective annual rate.

Given data

• Nominal rate = 6% p.a., compounding m = 2 times per year

Concept/ApproachEffective rate r_eff = (1 + r÷m)^m − 1.

Step-by-step calculationr_eff = (1 + 0.06÷2)² − 1 = (1.03)² − 1 = 1.0609 − 1 = 0.0609 = 6.09% p.a.

Common pitfallsMultiplying 6% by 2% directly is wrong; compounding must be applied.