A car dealer offers to sell a car for $10,000.$ The current market loan rate is a effective annual rate of

interest of $8\%.$ As an inducement, the dealer offers $100\%$ financing at an nominal interest rate of $6\%$ per

annum compounded monthly.

The loan is to be repaid in equal installments at the end of each month over a four$-$year period.

Calculate the cost to the dealer of this inducement. $($Hint: the cost is the difference between the cost of

car and the PV $($under the market loan rate$)$ of payments made by the car buyer.$)$