Problem: Suppose that a_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.
1) Derive a difference equation satisfied by a_n.
2) Solve the difference equation derived in (1) for a loan of £A to be repaid over N years and hence determine what the monthly repayment should be.
3) 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.
4) What is the total amount paid back on the loan?