Suppose you plan to put a $20\%$ down payment on a house and obtain a mortgage loan that is less than the size limit on conforming loans $($e$.$g$.$ $$417,000)$ to finance the remainder of the purchase. Based on your understanding of the loan$-$to$-$value ratio, what is the maximum price that you could pay for a home with these restrictions in mind?

$$2,085,000$

$$521\mathrm{.}250$

$$333,600$

$$500,400$