Esther pays $532 per month for 6 years for a car. she made a down payment of $3,700. if the loan costs 7.1% per year compounded monthly, what was the cash price of the car?

The amortization formula relates the principal and the loan payment by
  A = Pi/(n(1 -(1 +r/n)^(-nt)))
You have
  532 = P*0.071/(12*(1 -(1 +.071/12)^(-12*6))) = P*0.017097
  P = 532/0.017097 = 31,116.45

This was the amount financed, so the original price is 3700 higher.
  The cash price of the car was $31,116.45 +3,700 = $34,816.45