A car is purchased on hire purchase for $a. The debt is to be paid by a sequence of N payments over a total time of NT time periods. The interest charges are compounded at a rate r% per time period T.

What is the difference eqation representing this system?

My attempt:

Let y(k) = outstanding debt after the kth payment of p

y(k+1) = y(k) + r*y(k) - p

Is this correct? Where does the "a" come in?

Thanks