Imagine your favorite ocean$-$front house on Munster Beach becomes available for sale. You currently have $$50,000$ of savings ready to go$.$ Also, your monthly budget would allow to pay to $$500$ per month towards a $20-$year mortgage on this house. Finally, you are guaranteed to win the lottery in $10$ years from today, providing you with $$100,000$ at that time, and you can borrow against this money. Interest rates for any type of loan or investment sit at $5\%,$ compounded semiannually.

What is the maximum price you could afford to buy this house?