Assignment:
Q1. Miss X would like to take out a mortgage to buy a house in Leicester. The bank will charge her interest at a fixed rate of 6.1% per year compounded continuously. Miss X is able to pay money back continuously at a rate of £6000 per year.
• Make a continuous model of her economic situation, i.e. write a differential equation together with initial condition for the balance B(t) she owes the bank at time t.
• Say what the maximum mortgage Bo Miss X can take that she can replay in finite time.
• If the repayment period is 25 years, what is the maximum mortgage Bo Miss X can take?
Q2. Consider the functions 1, sin2x, cos2x.
• Write the Wronskian of these functions
• Evaluate the wronskian
• Are these functions linearly independent or linearly dependent? Explain why.
Provide complete and step by step solution for the question and show calculations and use formulas.