Pool$-$N$-$Patio World needs to borrow $$55,000$ to increase its inventory for the upcoming summer season. The owner is confident that he will sell most, if not all, of the new inventory during the summer, so he wishes to borrow the money for only four months. His bank has offered him a simple interest amortized loan at $7\frac{3}{4}\%$ interest. $($Round your answers to the nearest cent.$)$

$($a$)$ Find the size of the monthly bank payment.

$ $|$

$($b$)$ Prepare an amortization schedule for all four months of the loan.

$\backslash$table$[[\backslash$table$[[$Payment$],[$Number$]],\backslash$table$[[$Principal$],[$Portion$]],\backslash$table$[[$Interest$],[$Portion$]],\backslash$table$[[$Total$],[$Payment$]],\backslash$table$[[$Balance$],[$Due$]]],[0,,,,$$