Amortization Problem: A $30-$year, fixed$-$rate mortgage has an initial principal of $$500,000.$ The interest rate is $4\%$ per year compounded monthly. You must construct an amortization schedule showing the amount of interest and principal in each monthly payment. The amount of interest paid at End of Month $($EOM$)m$ depends on the principal owed at EOM $($m$-1).$ Furthermore, the amount of principal paid at EOM m is the difference between the monthly payment $($A$)$ and the amount of interest paid. The table below shows the first few rows of the amortization schedule. Your task is to construct the complete table for all $360$ months. You should use a spreadsheet to construct your table. If the house is sold immediately after the ${60}^{th}$ payment $($i$.$e$.,$ after $5$ years$),$ how much principal is still owed?

$\backslash$table$[[$EOM$,$Principal,$\backslash$table$[[$Interest$],[$Paid$]],\backslash$table$[[$Principal$],[$Paid$]],\backslash$table$[[$Total$],[$Payment$]]],[0,$$$500,000\mathrm{.}00,$$$0\mathrm{.}00,$$$0\mathrm{.}00,$$$0\mathrm{.}00$