Suppose a$10-$year, $ $1$ comma $000$ bond with an $8\mathrm{.}8\%$ coupon rate and$$ semi$-$annual coupons is trading for a price of $$$$1$ comma $034\mathrm{.}22.$

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

b$.$ If the$$ bond's yield to maturity changes to $9\mathrm{.}7\%$APR$,$ what will the$$ bond's price$$ be$?$