A $1,000$ bond with $6\%$ semiannual coupons is redeemable at $1,050$ in $20$ years. The

bond is selling for $975.$

$($a$)$ What is the nominal annual yield rate convertible semiannually to a purchaser who

buys the bond at this price?

$($b$)$ What price should be paid to earn a nominal annual rate of $7\%$ convertible semi$-$

annually?