4. (20 points) Financial applications of the Z-Transform (a) (5 points) An investment account starts with $1000, makes no other deposits, and has a balance of $2000 after 5 years. What key parameter can we know about how this account has been performing and what is its value? (b)(5 points) Show all of the details of a difference equation and its key parameters for a financial account that starts with $100, has deposits of $20 per month, and grows at a rate of 0.5% per month. Do not solve the equation. (c) (5 points) Consider the following engineering economics equation related to paying back a loan. P is the loan amount, r is the interest rate, and A is the regular payment. Assume payments and interest rates are monthly. A = P r(1+r) (1+r)" If a home is purchased for $200,000 and a loan is obtained for 360 months at an interest rate of 5% per year how much money will actually be paid for the home over the life of the loan? (d) (5 points) Some interest only loans allow only interest to be paid with no expectation of the home ever being paid off. From part (c), what would be the payment for the house if only interest was paid each month? 4. (20 points) Financial applications of the Z-Transform (a) (5 points) An investment account starts with $1000, makes no other deposits, and has a balance of $2000 after 5 years. What key parameter can we know about how this account has been performing and what is its value? (b)(5 points) Show all of the details of a difference equation and its key parameters for a financial account that starts with $100, has deposits of $20 per month, and grows at a rate of 0.5% per month. Do not solve the equation. (c) (5 points) Consider the following engineering economics equation related to paying back a loan. P is the loan amount, r is the interest rate, and A is the regular payment. Assume payments and interest rates are monthly. A = P r(1+r) (1+r)" If a home is purchased for $200,000 and a loan is obtained for 360 months at an interest rate of 5% per year how much money will actually be paid for the home over the life of the loan? (d) (5 points) Some interest only loans allow only interest to be paid with no expectation of the home ever being paid off. From part (c), what would be the payment for the house if only interest was paid each month