discount factor = $\frac{\text{price}}{\text{total cash flows (principal + remaining coupons)}}$

discount factor$_{6 \text{ months}}$ = $101.426 / (100 + 5.7 / 2)$discount factor${6 \text{ months}}$= `$101.426 / 102.85 = 0.98615$1`-year bond price = coupon${6 \text{ months}}$× DF${6 \text{ months}}$+ principal + coupon${12 \text{ months}}$× DF${12 \text{ months}}$`$102.64`2 = 7.5 \times 0.98615 + 107.5 \times \text{DF}{12 \text{ months}}$

$\text{DF}_{12 \text{ months}} = \frac{95.245875}{107.5}$
$\text{DF}_{12 \text{ months}} = 0.8860$

Note: we normally use discount factors to find the present value of future cash flows. In the case of bonds, the present value of future cash flows is the price.

price (present value) = total cash flows × discount factor