4. (20 points) Difference Equations (a) (5 points) A bank account accrues with an interest rate...

 

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4. (20 points) Difference Equations (a) (5 points) A bank account accrues with an interest rate r per year. It has no deposits or withdrawals after time n = 0. What is the difference equation for this discrete-time system? (b) (8 points) What yearly interest rate is needed for part (a) to have $2500 in 20 years? Assume a starting y[-1] = $1200. (c) (7 points) A different investment account has an interest rate of 6% per year and an input of $50 per month. The account has y[-1] = 0 and the following equations. What is the amount of money in the account after 5 years? Relevant equations for the system are below. h[n] (1.005)"u[n] x[n] = 50u[n] 4. (20 points) Difference Equations (a) (5 points) A bank account accrues with an interest rate r per year. It has no deposits or withdrawals after time n = 0. What is the difference equation for this discrete-time system? (b) (8 points) What yearly interest rate is needed for part (a) to have $2500 in 20 years? Assume a starting y[-1] = $1200. (c) (7 points) A different investment account has an interest rate of 6% per year and an input of $50 per month. The account has y[-1] = 0 and the following equations. What is the amount of money in the account after 5 years? Relevant equations for the system are below. h[n] (1.005)"u[n] x[n] = 50u[n]

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a The interest rate r is constant so the difference equation for this syst... View the full answer