Independent solution

How to solve this Step-Coupon Bond Pricing question

Setup

Setup

Let j be the common semiannual yield. Bond A pays 45 each half-year for 60 periods.

1,249.45=45a60‾∣j+1,000(1+j)−601{,}249.45=45a_{\overline{60}|j}+1{,}000(1+j)^{-60}

Model

Model

Solve the first price equation, then express Bond B as two 30-period coupon blocks plus redemption.

j=0.03499991j=0.03499991
PB=40a30‾∣j+50v30a30‾∣j+1,000v60P_B=40a_{\overline{30}|j}+50v^{30}a_{\overline{30}|j}+1{,}000v^{60}

Compute

Compute

At the recovered yield, the stepped coupons and redemption total 1190.25.

PB=1,190.253P_B=1{,}190.253

Answer

Answer

The listed price is 1190, choice E.

PB≈1,190(E)\boxed{P_B\approx1{,}190\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. 60 · N; 1249.45 · +/− · PV; 45 · PMT; 1000 · FV; CPT · I/Y3.499991This is the semiannual yield.