Monthly payment for a home: If you borrow $120,000 at an APR of 6% in order to buy a home, and if the lending institution compounds interest continuously, then your monthly payment M = M(Y ), in dollars, depends on the number of years Y you take to pay off the loan. The relationship is given by
a. Make a graph of M versus Y. In choosing a graphing window, you should note that a home mortgage rarely extends beyond 30 years.
b. Express in functional notation your monthly payment if you pay off the loan in 20 years, and then use the graph to find that value.
c. Use the graph to find your monthly payment if you pay off the loan in 30 years.
d. From part b to part c of this problem, you increased the debt period by 50%. Did this decrease your monthly payment by 50%?
e. Is the graph concave up or concave down? Explain your answer in practical terms.
f. Calculate the average decrease per year in your monthly payment from a loan period of 25 to a loan period of 30 years.