Assuming your house costs 8 gold and 50 silver the maximum payment is 7 gold and 245 silvers (90% of purchase price). For a deluxe it take about 39 weeks to max out. The button will stay greyed out until you have enough gold to unlock your home.
It would a nice enhancement if the game told you how much you need to unlock of the current instead of - not enough - keep adding silver - still not enough - more please.
You really do not want to use Mithril Coins. It takes 390 Mithril Coins to unlock my deluxe when it is capped at 90%. That works out to be 39 dollars or 1.65 silver per penny.
Note: My house has a 165 silver per week maintenance fee. The figures will change depending on the maintenance fee and sale price of your home.
Unless stated otherwise, all content in this post is My Personal Opinion.