Luke is borrowing $\$10{,}000$ from the bank. The bank offers him a choice between two $10$-year payment plans:${\bf Plan~1.}$ Luke's debt accumulates $10\%$ annual interest which compounds quarterly. Luke pays off half his balance after $5$ years, and the rest at the end of the $10$ years.${\bf Plan~2.}$ Luke's debt accumulates $10\%$ annual interest which compounds annually. Luke pays off his full balance at the end of the $10$ years.What is the (positive) difference between Luke's total payments under Plan 1 and his total payments under Plan 2? Round to the nearest dollar.