P66795A 5 4. Sarah takes out a mortgage of £155 000 to buy a house. Interest is added each month on the outstanding balance at a constant rate of r % each month. Sarah makes fixed monthly repayments to reduce the amount owed. Each month, interest is added, and then her monthly repayment is used to reduce the outstanding amount owed. The recurrence relationship for the amount of the mortgage outstanding after n + 1 months is modelled by un +1 = 1.0025un − x            n  0 where £un is the amount of the mortgage outstanding after n months and £x is the monthly repayment. (a) State the value of r. (1) (b) Solve the recurrence relation to find an expression for un in terms of x and n. (5) Given that the mortgage will be paid off in exactly 30 years, (c) determine, to 2 decimal places, the least possible value of x. (3) (Total for Question 4 is 9 marks) TOTAL FOR DECISION MATHEMATICS 2 IS 40 MARKS END P66795A 6 BLANK PAGE P66795A 7 BLANK PAGE P66795A 8 BLANK PAGE Turn over Pearson Edexcel Level 3 GCE Candidate surname Other names Total Marks Centre Number Candidate Number Please check the examination details below before entering your candidate information Paper reference P66795A ©2021 Pearson Education Ltd. 1/1/1/1/1/ 8FM0/28 Answer Book Do not return the question paper with the answer book. Further Mathematics Advanced Subsidiary Further Mathematics options 28: Decision Mathematics 2 (Part of option K only)