Sam Hinds, a local dentist, is going to remodel the dental reception area and two new workstations. He has contacted A$-$Dec, and the new equipment and cabinetry will cost $$18,000.$

A$-$Dee will finance the equipment purchase at $7\mathrm{.}5\%$ over a six$-$year period. A$-$Dec offers the dentist his choice of three payment options:

$($a$)$ Calculate the interest $(7\mathrm{.}5\%$ per year$)$ and principal under the discount loan option. $(2$ marks$)$

$($b$)$ Calculate interest at the rate of $7\mathrm{.}5\%$ per year for four years and then a final payment of interest and principal at the end of the $6$th year. Under the Interest Only loan option. $(2$ marks$)$

$($c$)$ Calculate the five equal payments at the end of each year inclusive of interest and part of the principal under the Amortized Loan option. $(2$ marks$)$

$($d$)$ Under which of the three options will the dentist pay the least interest and why? $(2$ marks$)$

$($e$)$ If the dentist decides to go with the amortized loan option, and after having paid two payments decides to pay off the balance. Using an amortization schedule, calculate his payoff amount. $(12$ marks$)$