Independent solution

How to solve this Bond Pricing and Yields question

Setup

Setup

Write the two six-period prices with common coupon and yield.

90.17=4a6‾∣j+Xv690.17=4a_{\overline6|j}+Xv^6
132.47=4a6‾∣j+1.6Xv6132.47=4a_{\overline6|j}+1.6Xv^6

Model

Model

Multiply the first equation by 1.6 and subtract the second to eliminate X.

1.6(90.17)−132.47=2.4a6‾∣j1.6(90.17)-132.47=2.4a_{\overline6|j}

Compute

Compute

The annuity factor is 4.917500, implying half-year rate 5.9989% and nominal annual rate 11.9977%.

a6‾∣j=4.91750000a_{\overline6|j}=4.91750000
i(2)=2j=0.11997726i^{(2)}=2j=0.11997726

Answer

Answer

The nominal annual yield is 12%, selecting choice E.

i(2)=12%(E)\boxed{i^{(2)}=12\%\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVM · 6 · N · 4.917500 · +/- · PV · 1 · PMT · 0 · FV · CPT · I/YI/Y = 6.00Solve the annuity factor as the price of six unit payments.