You buy a house for $$300,000,$ and take out a $30-$year mortgage at $7\%$ interest.

For simplicity, assume that interest compounds continuously.

Round all answers to $2$ decimal places.

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