Question $4(3$ points$)$ The following represents the yield curves of two bonds. One is treasury bond with no default risk. Another is B$-$rated corporate bond with default risk, and it has zero recovery value when default occurs. a$.(1$ pt$)$ What are the prices of the $20-$year$-$maturity zero$-$coupon treasury bond and the corporate bond respectively? Suppose face values are $1\mathrm{.}2$ million for both. b$.(1$ pt$)$ Find the cumulative default probability of the corporate bond $\backslash (\backslash$mathrm$\{$cp$\}(1),\backslash$mathrm$\{$cp$\}(2)\backslash ),$ and $\backslash (\backslash$operatorname$\{$cp$\}(20)\backslash ).$ c$.\backslash ((1\backslash$mathrm$\{$pt$\})\backslash )$ Find the marginal default probability of the corporate bond over the three time periods $\backslash (\backslash$mathrm$\{$p$\}(0,1),\backslash$mathrm$\{$p$\}(1,2)\backslash ),$ and $\backslash (\backslash$mathrm$\{$p$\}(2,20)\backslash ).$