Independent solution

How to solve this Cross-Frequency Bond Pricing question

Setup

Setup

Bond Z's quarterly coupon rate equals the nominal yield rate, so its price is par. Convert the quarterly yield to semiannual and annual effective rates.

PZ=1,000P_Z=1{,}000
js=(1.015)2−1=0.030225j_s=(1.015)^2-1=0.030225
ia=(1.015)4−1=0.06136355i_a=(1.015)^4-1=0.06136355

Model

Model

The price differences give P_Y = 1073.78 and P_X = 934.90. Use Bond Y's premium to identify its semiannual term.

73.78=(34−1,000js)a2n‾∣js73.78=(34-1{,}000j_s)a_{\overline{2n}|j_s}
2n=30,n=152n=30,\qquad n=15

Compute

Compute

Price Bond X over the 15-year annual schedule and solve for R.

934.90=Ra15‾∣ia+1,000(1+ia)−15934.90=Ra_{\overline{15}|i_a}+1{,}000(1+i_a)^{-15}
R=54.6005R=54.6005

Answer

Answer

The annual coupon is 54.60, choice E.

R≈54.60(E)\boxed{R\approx54.60\quad\text{(E)}}