A bank has made a $3-$year $$10$ million dollar loan that pays annual interest of $8\%.$ The principal is due at the end of the third year.

A$.$ The bank is willing to sell this loan with recourse at $8\mathrm{.}5\%$ discount rate. What should it expect for selling this loan?

B$.$ It also has the option of selling this loan without recourse at a discount rate of $8\mathrm{.}75\%.$ What should it expect for selling this loan?

C$.$ If the bank expects a $1/2\%$ probability of default on this loan, is it better off selling this loan with or without recourse? It expects to receive no interest payments or principal if the loan is defaulted.

D$.$ Why do you think that the interest rate in part A is different from the interest rate in part B$?$

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