Assume we have a PLAM for a $$450,000$ mortgage with a $30-$year term and monthly payments. The $$real$$ loan rate is $4\%,$ with inflation rates of $6\%,5\%,$ and $4\%$ for years $1,2,$ and $3,$ respectively. The inflation adjustments to the loan balance are assumed to be made annually. What is the loan balance at the beginning of year $2?$

Group of answer choices

None of the given answers

$472,214$

$468,600$

$472,412$

$476,832$