Esther pays $355 per month for 5 years for a car. She made a down payment of $2,500. If the loan costs 7.1% per year compounded monthly, what was the cash price of the car? I really just need the formula. I can't for the life of me figure it out!

The cash price of the car includes the amount of the loan plus the amount of the down payment

Cash price=the loan of the car+down payment

First find the amount of the loan by using the formula of the present value of an annuity ordinary which is

Pv=pmt [ (1 - (1+r/k) ^ (-kn)) : (r/k) ]

Pv the amount of the loan?

PMT payment per month 355

R interest rate 0.071

K compounded monthly 12

N time 5years

Pv=355 * ((1 - (1+0.071:12) ^ (-12

*5)) : (0.071:12))

=17,885.56

Cash price=17,885.56+2,500

=20,385.56 ... answer