Year 12: Financial Mathematics

5 dot points across 5 inquiry questions, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How do simple and compound interest accumulate value over time, and how do we move money between present and future?

Use simple and compound interest formulas to find future values, present values, interest rates and time periods

Simple and compound interest. The two formulas, conversion between annual and per-period rates, present and future value calculations, and the effect of compounding frequency, with worked examples.

15 min read →

How do equal regular contributions to an investment grow over time, and what is the future value formula for an annuity?

Derive and use the future value formula for an annuity to find the accumulated value of a series of equal regular contributions

Future value of an annuity. Derive the formula as a geometric series, apply it to regular savings, and solve for the required contribution or number of periods, with worked examples.

15 min read →

How do geometric sequences and series model repeated payments and recurring growth, and when does an infinite series converge?

Use the formulas for the nth term and the sum of n terms of a geometric sequence, and the limiting sum, in financial contexts

Geometric sequences and series in finance. The general term, finite sum, limiting sum and the convergence condition, applied to repeated deposits, depreciation and perpetuities, with worked examples.

14 min read →

How do arithmetic sequences and series model quantities that grow by a fixed amount each period, such as simple interest, salary rises and straight-line depreciation?

Use the formulas for the nth term and the sum of n terms of an arithmetic sequence in financial and modelling contexts

Arithmetic sequences and series. The common difference, the nth term, and the two partial-sum formulas, applied to simple interest, salary increments, fixed depreciation and stacked schedules, with worked examples.

14 min read →

How are reducing-balance loan repayments calculated, and how much of each payment goes to interest versus principal?

Use recurrence relations and the present value of an annuity to find loan repayments, outstanding balances and total interest paid

Loan repayments. Recurrence model for the outstanding balance, closed-form for the repayment via the present value of an annuity, splitting payments into interest and principal, and total interest, with worked examples.

16 min read →