The problem describes a debt to be amortized. $($Round your answers to the nearest cent.$)$Sean Lee purchases $$30,000$ worth of supplies for his restaurant by making a $$4,000$ down payment and amortizing the remaining cost with quarterly payments over the next $5$ 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.