Independent solution

How to solve this Coupon Bond Price Relations question

Setup

Setup

Let F be the second bond's face value, i its annual yield, and v the annual discount factor.

1,000vn=8901{,}000v^n=890
vn=0.89v^n=0.89

Model

Model

The second bond's annual coupon is Fi divided by 2. Price its coupons and redemption at the common yield.

890=Fi2an‾∣i+Fvn890=\frac{Fi}{2}a_{\overline n|i}+Fv^n

Compute

Compute

Use i times a-angle-n equals one minus v to the n, then insert 0.89.

890=F2(1−0.89)+0.89F890=\frac F2(1-0.89)+0.89F
F=8900.945=941.799F=\frac{890}{0.945}=941.799

Answer

Answer

The second face value is approximately 942, choice B.

F≈942(B)\boxed{F\approx942\quad\text{(B)}}