The payment plan the dealer offered Harold is an "installment plan with a down payment."
The expression for the amount of Harold’s last payment would be x - 100y.
In an "installment plan with a down payment," Harold is given the option to pay the purchase price of x dollars at a rate of 100 dollars per month for y months. Typically, such plans involve making regular fixed payments over a specified period, in this case, y months, with a down payment of 100 dollars per month.
At the end of the installment period, Harold pays the remaining balance amount. Since he has already paid 100 dollars per month for y months, the total amount paid up to that point would be 100 × y = 100y dollars.
The remaining balance would then be the total purchase price (x dollars) minus the total amount already paid (100y dollars), which gives us the expression for the amount of Harold’s last payment as x - 100y dollars. This amount covers the remaining balance after the installment payments have been made.