A firm has a corporate bond of $30-$year maturity has a face value of $$100$ and promises semi$-$annual coupon payments of $$3.$ The yield to maturity of $30-$year government bond is $5\%.$ On the maturity date, the firm has a probability of $50\%$ default. When that happens, the firm pays coupon and only pay $30\%$ of face value $.$ What should be the promised yield to maturity of this corporate bond? What is the yield spread?