Luke is borrowing $\$10{,}000$ from the bank. The bank offers him a choice between two $10$-year payment plans: 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. 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