Suppose that a house loan of $1,000,000 is to be paid off by equal monthly payments of $ d over the course of 30 years. Suppose that the loan accrues interest at a rate of 1%, compounded monthly. Let Yn be the amount of money owed at the beginning of the n-th month; thus, yo = 1,000,000 and the first payment and first interest charge both occur at time n = 1. (a) Show that the causal sequence yn satisfies yn = 1.014n-1 +1,000,0008,-dun-1. (b) Use the 2-transform to solve for yn (c) Set Y360 = 0 in order to solve for d. (d) What is the total sum of payments made over the 30 years?

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