Suppose a $10-$year, $$$$1000$ bond with a coupon rate of $8\mathrm{.}2\%$ and semiannual coupons is trading for $$$$1035\mathrm{.}47.$

a$.$ What is the$$ bond's yield to maturity$($expressed as an APR with semiannual$$ compounding$)?$

b$.$ If the$$ bond's yield to maturity changes to $9\mathrm{.}5\%$APR$,$ what will be the$$ bond's price?