Pablo wants to expand his successful automotive painting business in Winnipeg, MB$.$ To meet the needs of his growing customer base, he wants to purchase more painting equipment and install a down$-$draft painting booth, which will help him dry paint safely and quickly. The total cost will be $$87000\mathrm{.}00.$ The business has $$12000\mathrm{.}00$ in cash available to spend. Pablo has been offered the following loans by various financial institutions.

$\backslash$table$[[$COMPOUND INTEREST RATES AND TERMS$],[$Institution$,$Interest rate,Term$],[$Bank A$,8\mathrm{.}00\%,$ compounded annually,$3$ years$],[$Bank B$,7\mathrm{.}75\%,$ compounded annually,$4$ years$],[$Credit union C$,7\mathrm{.}00\%,$ compounded annually,$5$ years$],[$Credit union D$,6\mathrm{.}50\%,$ compounded annually,$6$ years$]]$

a$)$ Calculate the best loan deal for Pablo. Show work for all $4$ loans.

Bank $A$

$q,$ D$.$

b$)$ What would be the monthly payment at each institution?

c$)$ Which institution should Pablo choose? Explain your reasoning.