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# Differential Equations : Rate of Change Application Problem and Wronskian

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1) 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.
? What is the maximum mortgage Miss X can take that she can replay in finite time?
? If the repayment period is 25 years, what is the maximum mortgage Miss X can take?

2) Consider the functions 1.

? Write the Wronskian of these functions
? Evaluate the Wronskian
? Are these functions linearly independent or linearly dependent? Explain why.

##### Solution Summary

A Rate of Change Application Problem and Wronskian are solved . The solution is detailed and well presented.

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1) 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 ...

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