A used car dealer advertises financing at 0% interest over 3 years with monthly payments. You must pay a processing fee of $500 at signing. The car you like costs $9000.

a) What is your effective annual interest rate?

b) You believe that the dealer would accept $8200 if you paid cash. What effective annual interest rate would you be paying, if you financed with the dealer?

I have the solution that my professor provided, but it is missing details. Please answer with as much detail as possibe.

Solution provided by professor:

a) The monthly payments are $9,000/36 = $250 (over 3 years). NPW = 0 = $9,000 $500 $250 (P/A, i%, 36), so, (P/A, i%, 36) = 34.

i =0.25%, NPW = $96.50; i =0.50%, NPW = -$282.30

So, i = 0.314, so, ia = (1 + 0.00314)12 1 = 0.0383 or 3.83%.

b) The fact that the dealer would accept $8,200 cash for the car indicates its true worth so the extra $800 is a hidden finance charge. Your payments are still based on the original $9,000 cost but you only receive a car worth only $8,200!

NPW = 0 = $8,200 $500 $250 (P/A, i%, 36), so, (P/A, i%, 36) = 30.8 and

At i = 0.75%, NPW = 161.80 and at i =1.0%, NPW = -173.00,

so i = 0.871% ia = (1 + 0.00871)12 1 = 10.97%