Independent solution

How to solve this Bond Pricing and Yields question

Setup

Setup

Use half-year periods at yield 3.5%; the coupon amounts are 75 and 60.

PX=75a40‾∣0.035+Cv40P_X=75a_{\overline{40}|0.035}+Cv^{40}
PY=60a40‾∣0.035+(C+K)v40P_Y=60a_{\overline{40}|0.035}+(C+K)v^{40}

Model

Model

Subtract the prices so the unknown common redemption component cancels.

257.18=15a40‾∣0.035−Kv40257.18=15a_{\overline{40}|0.035}-Kv^{40}

Compute

Compute

The coupon present-value difference is 320.33 and v to the fortieth is 0.25257247; hence K = 250.01.

K=15a40‾∣0.035−257.18v40=250.011751K=\frac{15a_{\overline{40}|0.035}-257.18}{v^{40}}=250.011751

Answer

Answer

The redemption increment is approximately 250, selecting choice E.

K≈250(E)\boxed{K\approx250\quad\text{(E)}}