You have the following Yields on Securities in Percent

US Treasuries $($i$)1-$year Discount Bonds $($k$)$

$1-$year $5\mathrm{.}007\mathrm{.}75$

$2-$year $5\mathrm{.}759\mathrm{.}80$

a$.$ Calculate the one$-$year forward rate on the Treasuries and the corporate bond.

b$.$ Using the current and forward one$-$year rates, calculate the marginal probability of repayment on the corporate bond in years $1$ and $2,$ respectively.

c$.$ Calculate the cumulative probability of default on the corporate bond over the next two years.