Question $2(4$ points$)$ ABC bank is planning to make a loan of $\backslash (3,000,000\backslash )$ to SDSC department to buy quantum computing equipment. It expects to charge a servicing fee of $30$ basis points. The loan has a maturity of $8$ years with a duration of $7\mathrm{.}5$ years. The cost of funds $($the RAROC benchmark$)$ for the bank is $10$ percent. The bank has estimated the maximum change in the risk premium on the financial service sector to be approximately $4\mathrm{.}2$ percent, based on two years of historical data. The current market interest rate for loans in this sector is $10$ percent. a$.(1$ pt$)$ Using the RAROC model, determine whether $\backslash ($ A B C $\backslash )$ bank should make the loan. b$.(1$ pt$)$ What should be the duration in order to approve this loan? c$.\backslash ((1\backslash$mathrm$\{$pt$\})\backslash )$ Assuming that the duration cannot be changed, how much additional interest and fee income will be necessary to make the loan acceptable? d$.\backslash ((1\backslash$mathrm$\{$pt$\})\backslash )$ Given the proposed income stream and the negotiated duration, what adjustment in the loan rate would be necessary to make the loan acceptable?