Independent solution

How to solve this Bond Pricing question

Setup

Setup

Let v be the half-year discount factor and let 2n be the number of semiannual periods. The yield per half-year is 3.5%.

j=0.07/2=0.035j=0.07/2=0.035
v=(1.035)−1v=(1.035)^{-1}

Model

Model

Bond X pays 50 more coupon each half-year, while Bond Y pays 50 more at redemption. Subtracting their prices removes the unknown common redemption value.

969.52=50a2n‾∣0.035−50v2n969.52=50a_{\overline{2n}|0.035}-50v^{2n}
969.52=500.035(1−v2n)−50v2n969.52=\frac{50}{0.035}(1-v^{2n})-50v^{2n}

Compute

Compute

Isolating the maturity discount factor gives 0.3104696. Taking logarithms converts the number of half-years to years.

v2n=0.3104696v^{2n}=0.3104696
n=−ln⁡(0.3104696)2ln⁡(1.035)=17.0003n=\frac{-\ln(0.3104696)}{2\ln(1.035)}=17.0003

Answer

Answer

The bonds mature in 17 years, so the correct answer is choice B.

n=17(B)\boxed{n=17\quad\text{(B)}}