silly loan question - driving me nuts!

Colin buys a new car worth $25,000. He pays a 10% deposit (i.e $2500) and agrees to pay $500 at the end of each month for as long as necessary.
If interest is at 14% pa effective, find:

1. the number of payments of $500 requires
2. the amount of the final smaller payment required one month after the last full payment of $500
3. the loan outstanding after 2 years using both the retrospective and prospective methods

please see the attached working out for part 1, the answer is 62 but i am confused on how to get to that.

i_effective=14% (compounded monthly) ==> i_nominal = 13.17% compounded monthly.
Use Pv=$25000-$2500=$22500, i=13.17%, pmt=$500, Fv=$0 ==> n=62.4 months
Use n=62 months, pmt=$500, Pv=$22500, i=13.17% ==> Fv=$196.99 to be paid 1 month after the last $500 at n=63

Pv=Present value
Fv=Future value

Where does your thumbnail solution come from?
Completely wrong...your teacher drank a 40-ouncer of Canadian Club?
84 * 500 = $42,000 : would you pay that back after getting $22,500?!
Max gave you correct solution...

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Are you a loan officer...drumming up business?