A woman purchased a new car today for $$16,000.$ She paid $$2,000$ down and

borrowed the rest of the money. To repay the loan she agreed to make $16$

quarterly installments of $$750,$ with the first to be paid $3$ months from now, and a

final balloon payment at the end of the $16$ th quarter. The interest rate is $15\frac{\%}{y}r,$

compounded monthly. What is the effective quarterly rate?