To build a new warehouse, Whole Foods International signed a $$300,000$ simple interest note at $9\%$ for $150$ days with National Bank on November $20.$ On February $6,$ National Bank sold all of its notes to Bank One. Find the proceeds to National Bank given a discount rate of $10\mathrm{.}5\%.$ Assume a $360-$day year. $($Be sure your calculator date worksheet is set to a $360-$day year.$)$