Initiating an early payment discount Gardner Company currently makes all sales on credit and offers no discount. The firm is considering offering a $5\%$ discount for payment within $30$ days. The firm's current average collection period is $60$ days, sales are $40,000$ units per month, selling price is $$48$ per unit, and variable cost per unit is $$36.$ The firm expects that the change in credit terms will result in an increase in sales to $42,000$ units, that $70\%$ of the customers $($and $70\%$ of the dollar volume of sales$)$ will take the discount and pay on day $30,$ and the other customers will continue to pay the full invoice on day $60.$ The company's cost of capital is $0\mathrm{.}5\%$ per month. Should it offer the discount? $($Note: Assume a $365-$day year.$)$

The additional profit contribution from additional sales is $ $q,($Round to the nearest dollar.$)$