Sherry and Sam want to purchase a condo on the beach. They will spend $$650,000$ on the condo and are taking out a loan for the condo for $20$ years at $7\mathrm{.}0\%$ interest.

a$.$ What is the monthly payment on the mortgage? $(2$pts$)$ Construct the amortization of the loan for the $20$ years in Excel to show the monthly interest costs, the principal reduction, and the ending balance for each month. $(13$ points$)$

b$.$ Then change the amortization to reflect that after $10$ years, Sherry and Sam will increase their monthly payment to $$7500$ per month $(7$ points for spreadsheet$).$ When will they fully repay the mortgage with this increased payment if they apply all the extra dollars above the original payment to the principal?$(3$ points$)$