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HKSI PrepStudyingPaper 1
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Bank X offers 5.00% a year compounded semi-annually. Bank Y offers 5.05% a year compounded annually. Which deposit pays the higher effective annual rate?
Compare deposits on their effective annual rates, EAR = (1 + r/m)^m − 1. Bank X: (1 + 0.05/2)^2 − 1 = 1.025^2 − 1 = 0.050625, about 5.06%. Bank Y compounds once a year, so its EAR equals its nominal rate, 5.05%. Bank X therefore pays more, although its quoted rate is lower. Choosing Bank Y for its higher quoted rate ignores compounding. Saying Bank X's EAR is 5.00% treats its nominal rate as effective. Saying both pay 5.05% assumes the two compounding bases give the same result, which they do not. Source: Standard interest rate concepts (effective annual rate) (as at October 2026).
Comparing quoted rates with different compounding. Convert each to an effective annual rate first.
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