Independent solution

How to solve this Bonds with Mixed Coupon Frequencies question

Setup

Setup

Bond Z's coupon rate equals the quoted semiannual yield, so it is priced at par. Convert the common yield to quarterly and annual effective rates.

PZ=1,000P_Z=1{,}000
jq=(1.0325)1/2−1j_q=(1.0325)^{1/2}-1
ia=(1.0325)2−1i_a=(1.0325)^2-1

Model

Model

The price differences give P_Y = 1169.30 and P_X = 767.80. Bond Y's premium determines its number of quarterly periods.

169.30=(20−1,000jq)a4n‾∣jq169.30=(20-1{,}000j_q)a_{\overline{4n}|j_q}
4n=76,n=194n=76,\qquad n=19

Compute

Compute

Use the 19-year term to solve Bond X's annual-coupon price equation.

767.80=Ra19‾∣ia+1,000(1+ia)−19767.80=Ra_{\overline{19}|i_a}+1{,}000(1+i_a)^{-19}
R=44.2502R=44.2502

Answer

Answer

The annual coupon is 44.25, choice D.

R≈44.25(D)\boxed{R\approx44.25\quad\text{(D)}}