Suppose a

$1010-$year,

$$$$1$ comma $0001,000$

bond with a coupon rate of

$8\mathrm{.}1\%8\mathrm{.}1\%$

and semiannual coupons is trading for

$$$$1$ comma $034\mathrm{.}311,034\mathrm{.}31.$

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

$9\mathrm{.}7\%9\mathrm{.}7\%$

$$APR$,$ what will be the$$ bond's price?