1. 12 FURTHER MATHEMATICS Modelling and analysing reducing-balance loans and annuities

2. Analysing reducing-balance loans with recurrence relations Recurrence relations were used to model financial situations with linear and geometric growth and decay. These included simple and compound interest and the depreciation of assets. Recurrence relations can be used to model situations that involve elements of both linear and geometric growth.

3. Analysing reducing-balance loans with recurrence relations

4. Reducing-balance loans When money is borrowed from a bank, it is very unusual for the borrower to wait until the term of the loan is complete before paying all of the money owed, including the interest, back to the bank. Generally loans are repaid by making regular payments to reduce the amount owed, the balance of the loan, to zero over time. The amount originally borrowed is called the principal of the loan. This kind of loan is called a reducing-balance loan. A reducing-balance loan is effectively a compound interest loan, with regular payments. Personal loans and mortgages (home loans) are examples of reducing-balance loans.

5. Analysing reducing-balance loans with recurrence relations

14. WORK TO BE COMPLETED Exercise 9A All and 9B Odd Numbered Questions