$*$Use a financial calculator$*$: Max has a fixed$-$rate mortgage of $500,000$ wit a nominal rate compounding every $6$ months of $6\%$ amortized over $25$ years with monthly payment. The first term is $5$ years. Due to some special circumstance, Max and the lender have agreed: one, Max skips the regular payment that was supposed to be made at the end of$25$th month. This is the only payment missing. No more. Two, Max makes a prepayment of $1,000$ at the end of $36$th month. The $1,000$ prepay made is well below the allowable limit$.$ So$,$ what is the mortgage outstanding balance at the end of first term?