A Financial Institution $($FI$)$ has issued a one$-$year loan commitment of $$3$ million for an up$-$front fee of $25$ basis points. The back$-$end fee on the unused portion of the commitment is $10$ basis points. The FI$$s base rate on loans is $7\mathrm{.}5$ percent and the loan to this borrower carries a risk premium of $2\mathrm{.}5$ percent. The FI requires a compensating balance on loans of $5$ percent. Reserve requirement on demand deposit is $8$ percent.

Required:

a$.$ If the borrower draws down $75$ percent of the commitment at the beginning of the year, Calculate the dollar amount of total $($up$-$front and back$-$end$)$ fee income, interest income, compensating balance, reserve requirement on deposits, Funds committed $($used by borrower$)$ and the expected return on the loan $($without taking future values into consideration$).(6$ marks$)$

b$.$ If the borrower draws down $75$ percent of the commitment at the beginning of the fourth month, what is the expected return on the loan $($without taking future values into consideration$)?(4$ marks$)$

c$.$ Suppose that the expected return of loan commitments issued by this FI is $10\mathrm{.}85\%$ and the yield of Treasury bond is $7\%,$ what are the probability of repayment and the probability of default of this loan commitments? $(2$ marks$)$