Assume we have a $$500,000$ mortgage at a $3\mathrm{.}5\%$ original interest rate, $30-$year term, and monthly payments. The interest rate can be adjusted at the end of each year, and we assume the rate increases by $0\mathrm{.}25\%$ after the first year. What is the loan balance at the end of year $3?$

None of the given answers

$465,466$

$470,645$

$465,660$

$471,353$