The problem describes a debt to be amortized. $($Round your answers to the nearest cent.$)$

Sean Lee purchases $$40,000$ worth of supplies for his restaurant by making a $$2,000$ down payment and amortizing the remaining cost with quarterly payments over the next $4$ years. The interest rate on the debt is $16\%$ compounded quarterly.

$($a$)$

Find the size of each payment.

$

$($b$)$

Find the total amount paid for the purchase.

$

$($c$)$

Find the total interest paid over the life of the loan.