Consider a forward contract for a coupon bond. The spot price for the bond is currently $$950.$ The forward contract has two years to maturity and coupon payments of $$100$ are due in $6$ months and $18$ months$$ time. Continuously compounded risk$-$free interest rates $\%$ p$.$a are

$1$ month $=3\mathrm{.}5\%$

$6$ month $=4\%$

$12$ month $=4\mathrm{.}5\%$

$18$ month $=5\%$

$24$ month $=6\%$

The forward price to $2$ decimal places should be

$($a$)$ $$858\mathrm{.}66$

$($b$)$ $$856\mathrm{.}00$

$($c$)$ $$971\mathrm{.}41$

$($d$)$ $$855\mathrm{.}54$

$($e$)$ None of the above

The right answer is $($b$),$ how?