Independent solution

How to solve this Short Bond Yield question

Setup

Setup

The discount of 1.50 makes the purchase price 98.50. Each semiannual coupon is 3.

P=100−1.50=98.50P=100-1.50=98.50
C=100(0.06)/2=3C=100(0.06)/2=3

Model

Model

Let q be the effective yield per half-year.

98.50=31+q+103(1+q)298.50=\frac3{1+q}+\frac{103}{(1+q)^2}

Compute

Compute

The positive root is q = 0.03792935. Double it for the nominal annual yield convertible semiannually.

j=2q=0.0758587j=2q=0.0758587

Answer

Answer

The quoted nominal yield is approximately 0.076, choice D.

j≈0.076(D)\boxed{j\approx0.076\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2 · N; 98.5 · +/− · PV; 3 · PMT; 100 · FV; CPT · I/Y3.79294The display is the half-year yield; multiply by two for nominal j.