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?
Hello and thank you for posting your question to Brainmass!
The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, ...
The total payments over the life of the loan is demonstrated clearly.