Clear View Energy Systems is exploring borrowing $$500,000$ of additional short$-$term debt to help cover the start$-$up costs of a new product line. They$$re not sure if they will need all of it$,$ but they don$$t want to be caught short. You have been asked to evaluate a number of different short$-$term financing options to cover a period of about $9$ months. The options are as follows:

First National Bank has offered to loan you the $$500$K for $270$ days. The interest to be paid at maturity would be $$25,000.$

Second City Bank is offering a discounted loan of $$500$K for $270$ days with interest of $$23,000.$

Third$/$Fifth Bank is offering a $$500$K loan for $270$ days at an annual interest rate of $5\mathrm{.}5\%.$ The bank requires a compensating balance of $10\%$ of the amount loaned.

Fourth$-$But$-$Not$-$Last Bank is offering an installment loan of $$500$K with nine equal monthly payments of principal and interest. The total interest to be paid is $$18,000.$

Calculate $($and show$)$ the effective interest rate for each of these loan offers. Which one should you choose?