Archive / Investment Adviser (Level 1) / Time Value of Money

nism-series-xa-effective-annual-rate-semi-annual-coupon[ INVESTMENT ADVISER (LEVEL 1) ]

A corporate debenture pays an annual coupon of 8.0% p.a. distributed semi-annually. What is the Effective Annual Rate (EAR) earned by the bondholder?

[ A ]4.0% p.a.

[ B ]8.0% p.a.

[ C ]8.160% p.a.[ CORRECT ]

[ D ]8.976% p.a.

Takeaway

The Effective Annual Rate on the debenture is 8.160% p.a. — semi-annual compounding of the nominal 8% coupon produces a return slightly higher than the simple 8% nominal figure.

Derivation

Step 1: Semi-annual periodic rate = 8.0% / 2 = 4.0% per half-year. Step 2: EAR = (1 + r/m)^m - 1 = (1.04)^2 - 1 = 1.0816 - 1 = 0.0816 = 8.160% p.a. The 0.16-percentage-point gap between the quoted 8.0% nominal rate and the 8.160% effective rate is entirely the result of compounding the second half-year's interest on the first half-year's already-received interest — a small but real effect that grows sharply as compounding frequency increases (monthly, daily). This question tests whether candidates recognize that any nominal rate compounded more than once a year understates the investor's true annual return unless converted to EAR.

Why the others fail

A — 4.0% p.a.

4.0% is merely the semi-annual periodic rate (8%/2); it is not annualized and does not represent the bondholder's actual yearly effective return.

B — 8.0% p.a.

8.0% is the stated nominal annual coupon rate quoted before accounting for the effect of compounding twice a year — it understates the true effective return earned.

D — 8.976% p.a.

8.976% overstates the compounding effect for semi-annual payments — that figure would only arise from a materially higher compounding frequency or a calculation error, not (1.04)^2 - 1.