Suppose a$$ ten$-$year, $ $1,000$ bond with an $8\mathrm{.}5\%$ coupon rate and semiannual coupons is trading for $ $1,034\mathrm{.}36.$

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

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