Discussion

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:

Answer: D

The effective rate is the single annual rate that produces the same growth as the nominal rate does with its compounding.

Half-yearly payment at a nominal 6% means 3% every six months:

\[ (1.03)^{2} = 1.0609 \]

\[ \text{effective rate} = 1.0609 - 1 = 6.09\% \]

The extra 0.09% over the nominal 6% is the second half-year's 3% earned on the first half-year's 3% - the whole point of the effective-rate idea.

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