Year 12: Financial Mathematics

8 dot points across 8 inquiry questions, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How is compound interest calculated, and how do compounding frequency and time affect investment growth?

Use the compound interest formula to find future values, present values, interest rates and time periods for investments

Compound interest. The formula, conversion between annual and per-period rates, present and future values, the effect of compounding frequency, the recurrence-versus-formula comparison, and worked examples using current Australian bank rates.

13 min read →

How is depreciation calculated using the straight-line and declining-balance methods?

Use the straight-line and declining-balance methods to calculate the value of a depreciating asset over time

Depreciation. Both straight-line and declining-balance formulas, how they differ in shape, a year-by-year depreciation schedule built stage by stage, salvage value, solving for the rate, and worked Australian examples for cars, equipment and electronics.

11 min read →

How is credit card interest calculated, and how do the interest-free period and daily compounding affect the cost of using a credit card?

Calculate credit card interest using daily compounding, identify the interest-free period and the minimum monthly repayment

Credit card interest. Daily compounding from purchase date, the interest-free period if the balance is paid in full, the back-dating rule, the minimum-repayment trap, and worked Australian examples using typical RBA-published credit card interest rates.

12 min read →

What is the present value of an annuity, and how do future value and present value annuity tables let you find or back-solve a contribution?

Use future value and present value annuity tables, and calculate the present value of an annuity

The HSC Maths Standard 2 dot point on annuity tables and present value. What the present value of an annuity is, the link PV = FV / (1+r)^n, reading future-value and present-value annuity tables at the period by rate intersection, back-solving a contribution or rate from a table, converting an annual rate to the per-period row, and a loan as the present value of its repayments.

14 min read →

How is inflation measured by the Consumer Price Index, and how does it affect the real value of money and investments?

Use the Consumer Price Index to calculate inflation rates and compare real and nominal values over time

Inflation and the Consumer Price Index. The ABS CPI series over time, calculating total and annual inflation between two years, why inflation compounds, converting between real and nominal values, real returns, and worked Australian examples with current ABS data.

10 min read →

How does an annuity work, and how is superannuation modelled as a regular contribution growing at compound interest?

Use the future value formula for an annuity to find the accumulated value of regular contributions to superannuation or a savings plan

Annuities and superannuation. The future-value-of-annuity formula on the NESA reference sheet, why it is a geometric series, the future value built contribution by contribution, solving for the required payment, and worked Australian examples at current ATO Super Guarantee rates.

12 min read →

How are reducing-balance loan repayments calculated, and how does each repayment split between interest and principal?

Use recurrence relations and amortisation tables to calculate loan repayments, outstanding balances and the total interest paid on a reducing-balance loan

Reducing-balance loans. Recurrence model for the outstanding balance, building an amortisation table row by row, the recurrence-versus-formula comparison, the interest vs principal split of each payment, interest-only loans, and worked Australian mortgage examples at current RBA cash rate levels.

14 min read →

How are share investments analysed using dividends, yields and price-earnings ratios?

Calculate dividend yield, dividend payout, capital gain and total return on share investments

Shares. Dividend per share, dividend yield, brokerage, capital gain, total return as two combined sources, and the price-earnings ratio with worked Australian ASX examples.

10 min read →