Equity in a home: When you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. (Technically, the lending agency calculates your equity by...

Equity in a home: When you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. (Technically, the lending agency calculates your equity by subtracting the amount you still owe on your mortgage from the current value of your home, which may be higher or lower than your principal.) If your mortgage is forP dollars, and if the term of the mortgage is t months, then your equity E, in dollars, after k monthly payments is given by

Here r is the monthly interest rate as a decimal, with r = APR/12. Suppose you have a home mortgage of $400,000 for 30 years at an APR of 6%.

a. What is the monthly rate as a decimal? Round your answer to three decimal places.

b. Express, using functional notation, your equity after 20 years of payments, and then calculate that value.

c. Find a formula that gives your equity after y years of payments.