Solve the first-order linear difference equation xn+1 = Axn + B when A = 1 and...

 

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Solve the first-order linear difference equation xn+1 = Axn + B when A = 1 and when A 1. Make sure you show all calculations. [6 marks] b) By using the results in a), find what x, tends to as n→ +∞, when i) A=-1, B = 0; [2 marks] ii) A=0, B = 4; [2 marks] iii) A = 1/2, B = 1/4. [2 marks] Consider a loan of 300,000 Euro to be paid back over 30 years at a yearly interest rate of 1%, compounded once a year. Use the results in a) to calculate: i) The monthly repayment. [4 marks] ii) The total amount paid back. [1 mark] iii) The monthly repayment if the interest had been compounded every six months. [3 marks] Solve the first-order linear difference equation xn+1 = Axn + B when A = 1 and when A 1. Make sure you show all calculations. [6 marks] b) By using the results in a), find what x, tends to as n→ +∞, when i) A=-1, B = 0; [2 marks] ii) A=0, B = 4; [2 marks] iii) A = 1/2, B = 1/4. [2 marks] Consider a loan of 300,000 Euro to be paid back over 30 years at a yearly interest rate of 1%, compounded once a year. Use the results in a) to calculate: i) The monthly repayment. [4 marks] ii) The total amount paid back. [1 mark] iii) The monthly repayment if the interest had been compounded every six months. [3 marks]

Answer rating: 100% (QA)

a When A 1 xn1 xn B When A 1 xn1 Axn B b i When A 1 and B 0 xn1 xn The sequence will alternate betwe... View the full answer