c$)$ Consider a no$-$interest loan with current rating A$,$ maturity of $3$ years and amount to be repaid at maturity of $$100$ million. The recovery rate in case of default is $50\%$ of the repayment value. Assume a default probability of $2\mathrm{.}02\%$ and the following yield curve for an A$-$rated corporate:

$\backslash$table$[[$Time to maturity,$1$ year,$2$ years,$3$ years,$4$ years,$5$ years$],[$Spot rate,$2\mathrm{.}80\%,3\mathrm{.}01\%,3\mathrm{.}21\%,3\mathrm{.}73\%,3\mathrm{.}98\%$