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

Sean Lee purchases $$40,000$ worth of supplies for his restaurant by making a $$3,000$ down payment and amortizing the remaining cost with quarterly payments over the next $6$ 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.

$