Independent solution

How to solve this Bond Pricing and Yields question

Setup

Setup

Price the first bond from its annual coupon and redemption at the common 6.5% yield.

P=0.076(6000)a20‾∣0.065+6000(1.065)−20P=0.076(6000)a_{\overline{20}|0.065}+6000(1.065)^{-20}

Model

Model

Use that same market price for the second bond and solve for its annual coupon rate.

P=7500r a20‾∣0.065+7500(1.065)−20P=7500r\,a_{\overline{20}|0.065}+7500(1.065)^{-20}

Compute

Compute

The common price is 6727.22 and the second coupon is 417.37, giving r = 5.5649%.

r=0.05564872r=0.05564872

Answer

Answer

The second bond's coupon rate is approximately 5.6%, selecting choice A.

r≈5.6%(A)\boxed{r\approx5.6\%\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVM · 20 · N · 6.5 · I/Y · 456 · PMT · 6000 · FV · CPT · PVPV = -6727.22Annual coupon is 7.6% of 6,000.
  2. 20 · N · 6.5 · I/Y · 6727.22 · +/- · PV · 7500 · FV · CPT · PMTPMT = 417.37