Independent solution

How to solve this Bond Price Decomposition question

Setup

Setup

Express the coupon as redemption amount times coupon rate r and use i for the yield per coupon period. The supplied ratios r/i and vⁿ allow the price to be evaluated without solving separately for r, i, or n.

P=1000r a2n‾∣ i+Cv2nP=1000r\,a_{\overline{2n}|\,i}+Cv^{2n}

Model

Model

Price equals coupon present value plus discounted redemption. Rewriting the annuity factor as (1 − v²ⁿ)/i produces the displayed decomposition.

r/i=1.03125,vn=0.5889,Cv2n=381.50r/i=1.03125,\quad v^n=0.5889,\quad Cv^{2n}=381.50

Compute

Compute

The coupon component is 673.61 and the redemption component is 381.50, totaling 1,055.11. The listed value is 1,055.

P=1000(1.03125)(1−0.58892)+381.50=1055.11P=1000(1.03125)(1-0.5889^2)+381.50=1055.11

Answer

Answer

The calculation gives 1055 for bond price decomposition, matching published choice D.

P=1055(D)\boxed{P=1055\quad\text{(D)}}