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 :)