Dome Metals has credit sales of $$468,000$ yearly with credit terms of net $60$ days, which is also the average collection period. Assume the firm adopts new credit terms of $\frac{3}{10},$ net $60$ and all customers pay on the last day of the discount period. Any reduction in accounts receivable will be used to reduce the firm's bank loan which costs $8$ percent. The new credit terms will increase sales by $20\%$ because the $3\%$ discount will make the firm's price competitive.

a$.$ If Dome earns $20$ percent on sales before discounts, what will be the net change in income if the new credit terms are adopted?

Note: Use a $360-$day year.

Net change in income