A $5\%$ bond maturing in $20$ years with semiannual coupons and semiannual yield rate of $3\%$ is toreplaced by a$20$ year bond also with semiannual coupons and semiannual yield rate of $5\%.$ If both bonds have the same price and face value then find the semiannual coupon rate of the second bond.

A $5\%$ bond maturing in $20$ years with semiannual coupons and semiannual yield rate of $3\%$ is to replaced by a $20$ year bond also with semiannual coupons and semiannual yield rate of $5\%.$ If both bonds have the same price and face value then find the semiannual coupon rate of the second bond.