Suppose a$$ ten$-$year, $$1,000$ bond with a $8\mathrm{.}1\%$ coupon rate and semiannual coupons is trading for $$1,034\mathrm{.}48.$

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?