Independent solution

How to solve this Yield from Equal Bond Prices question

Setup

Setup

First price the initial bond at its known 2.5% half-year yield. This establishes the common market price without using the second bond’s unknown yield.

P1=25a60‾∣ 0.025+1200(1.025)−60=1045.46P_1=25a_{\overline{60}|\,0.025}+1200(1.025)^{-60}=1045.46

Model

Model

Insert that price into the second bond’s sixty-period cash-flow equation and solve for its half-year yield j/2.

1045.46=25a60‾∣ j/2+800(1+j/2)−601045.46=25a_{\overline{60}|\,j/2}+800(1+j/2)^{-60}

Compute

Compute

The common price is 1,045.46 and the second yield is 2.2% per half-year. Hence the nominal annual yield is 4.40%.

j/2=0.022,j=0.044j/2=0.022,\quad j=0.044

Answer

Answer

The calculation gives 4.40% for yield from equal bond prices, matching published choice D.

j(2)=4.40%(D)\boxed{j^{(2)}=4.40\%\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 60 N; 2.5 I/Y; 25 PMT; 1200 FV; CPT PV−1045.46Common price from the first bond.
  2. 1045.46 +/- PV; 25 PMT; 800 FV; CPT I/Y; × 2 =4.40Nominal annual yield of the second bond.