Page 1: Loan Repayment Calculation
This page introduces a recurrence relation word problem focused on loan repayment calculations. It demonstrates how to use recurrence relations to model financial scenarios, a common topic in Higher Maths and A Level Maths.
The problem presents Betty's loan of £2000 with a 1.5% monthly interest rate and £450 monthly repayments. Students are tasked with creating a recurrence relation to model the loan balance over time.
Definition: A recurrence relation for this loan scenario is given as Bn+1 = 1.015Bn - 450, where Bn represents the balance after n months.
The page walks through the calculation process month by month, showing how the loan balance decreases over time. This step-by-step approach is valuable for students learning to apply recurrence relations to real-world problems.
Example: The calculation shows that by the end of May, the balance owed is £281.82058, and the final payment is made in June.
The problem also asks students to calculate the total amount Betty will have paid, which comes to £2086.05. This illustrates the concept of total interest paid on a loan, an important aspect of financial mathematics.
Highlight: For questions involving exceeding or dropping below specific limits, it's crucial to consider the values both before and after each payment or change.
This page effectively demonstrates the application of recurrence relations in financial contexts, providing a practical example that students might encounter in Higher Maths past papers or A Level Maths exams.
