Problem $4.$

You have finally saved up $5\%$ necessary to purchase a house. And because you are a good worker, you were able to get a raise and your new take home pay is $$5568\mathrm{.}00$ a month. Assuming an interest rate of $5\mathrm{.}75\%($rates went down while you were saving$)$ and a $30$ year loan, with continuous compounding interest, how much house could you afford $($don$\text{'}$t forget to account for the $5\%$ you put down$).$