Independent solution

How to solve this Callable Bond Redemption Value question

Setup

Setup

Work in semiannual periods: the yield is 3% per half-year and the earliest call date is 30 periods away. Let X be the redemption amount, so each coupon is 4% of X.

j=0.03,n=30j=0.03,\quad n=30

Model

Model

Price equals the present value of thirty coupons plus X at the call date. Both cash-flow components are proportional to X, leaving a direct linear equation.

1722.25=0.04Xa30‾∣ j+Xv301722.25=0.04X a_{\overline{30}|\,j}+Xv^{30}

Compute

Compute

Solving 1,722.25 = X[0.04a-angle-30 + v³⁰] gives X = 1,440.

X=1440X=1440

Answer

Answer

The calculation gives 1440 for callable bond redemption value, matching published choice C.

X=1440(C)\boxed{X=1440\quad\text{(C)}}