Independent solution

How to solve this Bond Valuation question

Setup

Setup

Move every investment cash flow to the ten-year horizon.

F10=500s10‾∣ 0.08+10000F_{10}=500s_{\overline{10}|\,0.08}+10000

Model

Model

Coupons accumulate at their 8% reinvestment rate and face is received at maturity.

F10=17243.28F_{10}=17243.28

Compute

Compute

The investor's purchase price must grow at the realized 8.5% yield to that same terminal value.

X(1.085)10=17243.28⟹X=7626.45X(1.085)^{10}=17243.28\Longrightarrow X=7626.45

Answer

Answer

The issue price is approximately 7,626, corresponding to choice A.

X≈7626(A)\boxed{X\approx7626\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 10 N; 8 I/Y; 0 PV; 500 +/- PMT; CPT FVFV coupons = 7243.28Add the 10,000 redemption to obtain terminal proceeds 17,243.28.
  2. 10 N; 8.5 I/Y; 0 PMT; 17243.28 FV; CPT PVPV = -7626.45