# total amount paid back on the loan

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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.

(i) Derive a difference equation satisfied by a_n.

(ii) Solve the difference equation derived in (i) for a loan of £A to be repaid over N years and hence determine what the monthly repayment 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?

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The total payments over the life of the loan is demonstrated clearly.

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