Consider a $100K, 15 year mortgage with 6.5% interest.

(a) Calculate the monthly payment (PMT), and then the monthly principal and interest payments as a fraction PMT. Plot these fractions as a function of the mortgage maturity (time). How long will it take before 50% of monthly payment (PMT) is applied toward the principal (be exact).

(b) Suppose the borrower increases her mortgage payment by s = 1% a month for the first 100 months, that is the payment for month t is PMT_t = PMT (1 + s/100 )^t , t = 1, ...., 100. How would this strategy effect the maturity of the loan and the total interest payments on the loan.

(c) Suppose the borrower decides to randomize her monthly payments. For the first 100 months, she will draw a number, s, from the uniform distribution with minimum 0 and maximum 1. Then her payment for any month will be PMT_t = PMT (1 + s), s U(0, 1). How would this strategy effect the maturity of the loan and the total interest payments on the loan. Compare your results with part (b). HINT: Use the Excel RAND() function to generate random draws for s U(0, 1).

(d) Suppose the borrower decides to randomize her monthly payments. For the first 100 months, she will throw the dice to draw a number, s = {1, 2, 3, 4, 5, 6}, each with equal probability ( 1/6 ), and will increase her payment by s percent. Then her payment for any month will be PMT_t = PMT (1 + s/100 ). How would you simulate this random outcome? How would this strategy effect the maturity of the loan and the total interest payments on the loan. Compare your results with parts (b) and (c).