Independent solution

How to solve this Midterm Bond Book Value question

Setup

Setup

There are 2n semiannual coupons in an n-year bond. Let x be the coupon and v = 1/1.02.

v=(1.02)−1v=(1.02)^{-1}

Model

Model

At the midpoint after coupon n, exactly n coupons remain.

95.5087=100vn+xan‾∣0.0295.5087=100v^n+xa_{\overline n|0.02}
xan‾∣0.02=95.5087−100vnxa_{\overline n|0.02}=95.5087-100v^n

Compute

Compute

Split the original 2n-period price into the first n coupons and the midpoint value, then eliminate x.

91.8243=95.5087vn+95.5087−100vn91.8243=95.5087v^n+95.5087-100v^n
3.6844=4.4913vn3.6844=4.4913v^n
n=10.0004n=10.0004

Answer

Answer

The term is 10 years, choice B.

n=10(B)\boxed{n=10\quad\text{(B)}}