Finance A $200,000 home mortgage for 30 years at 4.25% has a monthly payment of $983.88. Part of the monthly payment goes toward the interest charge on the unpaid balance, and the remainder of the payment is used to reduce the principal. The amount that goes toward the interest is given by u = M r 12t - (M-1) (1+1)" 12 12 and the amount that goes toward reduction of the principal is given by Pr r 12t -- (M-1) (1+1)**. v = 12 12 In these formulas, P is the amount of the mortgage, r is the interest rate, 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, the larger part of the monthly payment goes for what purpose? 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 = $1238.47). What can you conclude?