Independent solution

How to solve this Bond Book-Value Change question

Setup

Setup

The coupon rate exceeds yield, so book value declines toward face. The premium amortized in year t is the coupon-yield spread on the discounted redemption.

At=(g−i)Fvn−t+1A_t=(g-i)Fv^{n-t+1}

Model

Model

Use n = 20, t = 8, g = 0.08, and i = 0.04.

43.24=0.04F(1.04)−1343.24=0.04F(1.04)^{-13}
F=1,799.94F=1{,}799.94

Compute

Compute

Price twenty annual coupons and redemption at 4%.

P=0.08Fa20‾∣0.04+F(1.04)−20=2,778.42P=0.08F a_{\overline{20}|0.04}+F(1.04)^{-20}=2{,}778.42

Answer

Answer

The price rounds to 2780, choice D.

P≈2,780(D)\boxed{P\approx2{,}780\quad\text{(D)}}