Financial Math and Recursion Relations Student Workbook

Key knowledge

• the concept of an arithmetic or geometric sequence as a function and its recursive specification.
• the use of a first-order linear recurrence relation to generate the values of an arithmetic or geometric sequence.
• the explicit rule of an arithmetic or geometric sequence and its evaluation.
• the use of a first-order linear recurrence relations, including the rule for evaluating the value after n periods of linear growth or decay in financial contexts, simple interest investments and loans, flat rate and unit cost depreciation of an asset over time, including the rule for the future value of the asset after n depreciation periods.
• the use of first-order linear recurrence relations to model compound interest investments and loans, reducing balance depreciation of an asset over time, including the rule for the future value of the asset after n depreciation periods, compound interest investments and debts.
• concepts of ratio, proportion, percentage, percentage change and rate, and unitary method.

Key skills

• use a given recurrence relation to generate a sequence, deduce the explicit rule, from the recursion relation, tabulate, graph and evaluate the sequence
• use a recurrence relation, table or graph to model and analyse practical situations involving discrete linear growth or decay
• demonstrate the use of a recurrence relation to determine the linear depreciating value of an asset after time periods for the initial sequence
• use a rule for the future value of a linear depreciating asset to solve practical problems