a$.$ Many years ago, Castles in the Sand Incorporated issued bonds at face value at a yield to maturity of $5\mathrm{.}2\%.$ Now, with $5$ years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to $11\%.$ What is now the price of the bond? $($Assume semiannual coupon payments.$)$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Bond price

b$.$ Suppose that investors believe that Castles can make good on the promised coupon payments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only $80\%$ of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to $2$ decimal places.

Yield to maturity