A $120,000 home mortgage for 30 years at 7 1/2% has a monthly payment of $839.06. Part of the monthly payment covers the interest charge on the unpaid balance, and the remainder of the payment reduces the principal. The amount paid toward the interest is

and the amount paid toward the reduction of the principal is

In these formulas, P is the amount of the mortgage, r is the interest rate (in decimal form), M is the monthly payment, and t is the time in years.
(a) Use a graphing utility to graph each function in the same viewing window. (The viewing window should show all 30 years of mortgage payments.)
(b) In the early years of the mortgage, is the greater part of the monthly payment paid toward the interest or the principal? Approximate the time when the monthly payment is evenly divided between interest and principal reduction.
(c) Repeat parts (a) and (b) for a repayment period of 20 years (M = $966.71). What can you conclude?

Transcribed Image Text:

12г 12г и%3D М— (м м— 121 v = (M 12/ 12/