You buy a house for

$,$ and take out a

$-$year mortgage at

interest.

For simplicity, assume that interest compounds continuously.

Round all answers to $2$ decimal places.

What will be your annual mortgage payment?

per year

Suppose that regular raises at your job allow you to increase your annual payment by

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