Independent solution

How to solve this Bond Valuation question

Setup

Setup

Use half-year periods because coupons and the nominal yield share that conversion frequency.

P6=Ca6‾∣ 0.05+1000v6,P12=Ca12‾∣ 0.05+1000v12P_6=Ca_{\overline{6}|\,0.05}+1000v^6,\qquad P_{12}=Ca_{\overline{12}|\,0.05}+1000v^{12}

Model

Model

Express each bond price with the same coupon amount but six versus twelve payment periods.

P6−P12=49P_6-P_{12}=49

Compute

Compute

Subtract the longer-term price from the shorter-term price and solve the resulting linear equation in the coupon.

49=C(a6‾∣−a12‾∣)+1000(v6−v12)⟹C=3749=C(a_{\overline{6}|}-a_{\overline{12}|})+1000(v^6-v^{12})\Longrightarrow C=37

Answer

Answer

Each semiannual coupon is 37, which corresponds to choice A.

C=37(A)\boxed{C=37\quad\text{(A)}}