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I am having terrible trouble with the following question:

Suppose that $x_n$ is the amount owed on a mortgage after n years, £$m$ is the monthly repayment and $r$ is the annual percentage interest rate charged on the amount of the mortgage outstanding.

i) Derive a difference equation satisfied by $x_n$.

ii) Solve the difference equation derived in i) for a loan of $£m$ to be repaid over $N$ years and hence determine what the monthly payment should be.

iii) If the interest rate is 5% show that the monthly repayment on a loan of £50,000 to be repaid over $25$ years is £295.64.

iv) What is the total amount paid back on the loan?

Any help would be great thanks :)

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    What do you know about these sort of problems? What have you tried so far? We can be a lot more helpful if you let us know more specifically where you're stuck.2012-08-09
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    I am having problems deriving a difference equation from the information. Once I have an equation I should be able to solve it myself.2012-08-09
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    Welcome to Math.StackExchange! I've posted an answer for (i), so I hope that will get you started. Let me know if there's anything else that you could use help with.2012-08-09

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