Vicky spends $P$ to purchase a $15-$year, $1000-$par, bond that pays semiannual coupons at a coupon rate

of $3\%.$ Immediately after receiving coupon number $16,$ Vicky sells the bond to Nick for a price of $Q.$

The yield rate on Vicky's investment is $5\mathrm{.}5\%$ convertible semiannually and the yield rate on Nick's

investment is $4\%$ convertible semiannually. Calculate $P.$

$849$

$833$

$801$

$817$

$865$