Consider a $10-$year zero$-$coupon bond with a par value of $$1000.$ Suppose that investors believe that there is a $30\%$ probability that the issuer will default on its debt when the bond matures and if the issuer does default, investors will get $60\%$ of the par value. Further assume investors demand an expected rate of return from investing this bond that is two percentage points higher than the $10-$year T$-$bonds, which currently have a yield of $4\mathrm{.}3\%.$ We calculated in class that the price of the bond should be $$477\mathrm{.}69,$ and yield should be $7\mathrm{.}67\%.$ If investors now expect the default probability to be $50\%($while everything else stays the same$),$ what would be the bond's new price and yield? Are they higher or lower compared to before and why? $($shpw all your work clearly please$)$