Independent solution

How to solve this Bond Yields question

Setup

Setup

The bond pays 40 every half-year for 12 periods and redeems 1,000 at the end of period 12.

N=12N=12
C=1000(0.08)/2=40C=1000(0.08)/2=40

Model

Model

Let j be the half-year yield. Equate the quoted price to the coupon annuity plus discounted redemption value.

911.37=40a12‾∣j+1000(1+j)−12911.37=40a_{\overline{12}|j}+1000(1+j)^{-12}

Compute

Compute

Numerical solution gives j = 5%. Convert the half-year rate to an annual effective rate.

j=0.05j=0.05
i=(1.05)2−1=0.1025i=(1.05)^2-1=0.1025

Answer

Answer

The annual effective yield is 10.25%, which is choice E.

i=10.25%(E)\boxed{i=10.25\%\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVMTVM worksheet clearedUse half-year periods and END mode.
  2. 12 · NN = 12
  3. 911.37 · PVPV = 911.37
  4. 40 · +/- · PMTPMT = -40
  5. 1000 · +/- · FVFV = -1,000
  6. CPT · I/YI/Y = 5.0000
  7. 1.05 · × · 1.05 · = · − · 1 · =0.1025Convert the half-year yield to annual effective yield.