Independent solution

How to solve this Callable Discount Bond question

Setup

Setup

Use the earliest relevant call date of twenty half-year periods and a yield of 3% per half-year. Let X be the unknown redemption amount; each coupon equals 2% of X.

j=0.03,n=20j=0.03,\quad n=20

Model

Model

The bond’s price is X times the sum of the coupon-annuity factor and the discounted redemption factor. Because the coupon rate is below yield, the price is below X as expected.

1021.50=0.02Xa20‾∣ j+Xv201021.50=0.02X a_{\overline{20}|\,j}+Xv^{20}

Compute

Compute

Solving the linear price equation gives X = 1,200.

X=1200X=1200

Answer

Answer

The calculation gives 1200 for callable discount bond, matching published choice E.

X=1200(E)\boxed{X=1200\quad\text{(E)}}