You buy a house for $$250000,$ and take out a $30-$year mortgage at $6\mathrm{.}5\%$ interest.

For simplicity, assume that interest compounds continuously.

A$)$ What will be your annual mortgage payment?

$

per year

B$)$ Suppose that regular raises at your job allow you to increase your annual payment by $6\%$ each

year. For simplicity, assume this is a nominal rate, and your payment amount increases continuously.

How long will it take to pay off the mortgage?

years