[bebbeDaisy]

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?Really bad at deriving equations, so struggling with the first 2 parts of this question. tried to do part 3, however using the formula i could find for the amount payable, M = Pi/[q(1-[1+(i/q)]^-nq)], i got the monthly repayments to be 292.30 instead of 295.64.. the lecturer sent around an email saying 'Hint: In at least one of the solution attempts that I have seen, the annual interest rate was wrongly extended to the the monthly repayments' so i assume i did that, but dont know how to adapt it!Any help on this would be greatly appreciated.Thanksto david, i, and i assume a number of others, got the same as you for part 3, however this is the whole email that the lecturer sent aroundSome of you have asked me about Question 8, suggesting the £295.64 in part (iii) might be wrong. I have now looked at the numbers again, and I can confirm that the £295.64 on the assessment sheet are indeed correct.Hint: In at least one of the solution attempts that I have seen, the annual interest rate was wrongly extended to the the monthly repayments! Now that would be a really nice (or naive) bank that pays you interest for the instalments of your mortgage...