Consider a Bank Loan system whose state x[n] is the balance of a bank account at the beginning of month n, and u[n] is the amount deposited or withdrawn during month n.

(a) Suppose you open an account by taking out a loan of $10,000 with an interest rate of 1.5% per month. Determine the coefficients a and b in the next-state equation x[n + 1] = ax[n] + bu[n], and the initial state x[0], to model this scenario.

(b) Determine the monthly payment w if the term of the loan is 32 months. You may use the summation identity:

(c) Using your answer from (b), what is the total payment over the 32 months?

(d) Suppose that the interest rate is 0.5% less (1% rather than 1.5%). How much less in dollars would the total payment be over the 32 months of the loan?

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