HKSI Paper 7 The debt market question: effective annual rate

HKSI Paper 7The debt market

A bank quotes 8% a year, compounded quarterly, on a one-year deposit. What is the effective annual rate?

A 8.24%
B 8.30%
C 8.00%
D 8.16%

Show the answer and explanation

Answer: A. 8.24%

The effective annual rate (EAR) converts a quoted nominal rate into the rate actually earned over a year: EAR = (1 + r/m)^m − 1, where m is the number of compounding periods a year. Here r/m = 8% ÷ 4 = 2% a quarter, so EAR = (1.02)^4 − 1 = 1.0824 − 1 = 8.24%. 8.00% ignores compounding within the year; it is the nominal rate. 8.16% is (1.04)^2 − 1, which is semi-annual compounding. 8.30% is (1 + 0.08/12)^12 − 1, which is monthly compounding. Source: Standard interest rate concepts (effective annual rate) (as at October 2026).

Common mistake

Dividing the rate by the wrong number of periods. Quarterly means four periods of r ÷ 4, compounded four times.

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Original study material mapped to the public HKSI Paper 7 syllabus. Unofficial, not endorsed by HKSI Institute or the SFC. Verify figures and rules against current guidance before relying on them.