VCE Further Mathematics Units 3 and 4 – Recursion and Financial Mathematics

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Description

2.1 Recurrence Relations
2.2 Interest Rates
2.3 Borrowing Money
2.4 Annuity




Additional information

Outcome

Key knowledge
• the concept of a first-order linear recurrence relation and its use in generating the terms in a sequence
• uses of first-order linear recurrence relations to model growth and decay problems in financial contexts
• the use of first-order linear recurrence relations to model flat rate and unit cost, and reduce balance depreciation of an asset over time, including the rule for the future value of the asset after n depreciation periods
• the concepts of financial mathematics including simple and compound interest, nominal and effective interest rates, the present and future value of an investment, loan or asset, amortisation of a reducing balance loan or an annuity and amortisation tables
• the use of first-order linear recurrence relations to model compound interest investments and loans, and the flat rate, unit cost and reducing balance methods for depreciating assets, reducing balance loans, annuities, perpetuities and annuity investments.

Key skills
• use a given first-order linear recurrence relation to generate the terms of a sequence
• model and analyse growth and decay in financial contexts using a first-order linear recurrence relation
• demonstrate the use of a recurrence relation to determining the depreciating value of an asset or the future value of an investment or a loan after n time periods, including from first principles for n ≤ 5
• use a rule for the future value of a compound interest investment or loan, or a depreciating asset, to solve practical problems
• use a table to investigate and analyse on a step–by-step basis the amortisation of a reducing balance loan or an annuity, and interpret amortisation tables
• with the aid of technology with financial mathematics capabilities, solve practical problems associated with compound interest investments and loans, reducing balance loans, annuities and perpetuities, and annuity investments.

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