Mathematics 11–12 · Year 12

A reducing balance home loan and a credit card balance at current RBA rates

Financial mathematics: Reducing balance loans (Mathematics Advanced, Year 12); Investment and loans: Loans (Mathematics Standard 2, Year 12); Investment and loans: Credit cards (Mathematics Standard 2, Year 12); Depreciation and loans: Loans (Mathematics Standard 1, Year 12); Depreciation and loans: Credit cards (Mathematics Standard 1, Year 12)

Calculation and dataLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

Each month a loan balance grows by interest and falls by the repayment, so a spreadsheet of the reducing balance shows why early repayments are mostly interest and why extra repayments save so much.

What you need

RBA table F6: average rate on new owner-occupier variable-rate housing loans funded in July 2026, 6.2 per cent (series FLRHOFVA)
RBA table F5: banks' standard variable owner-occupier rate 8.77 per cent, and credit card rates 20.99 per cent (standard) and 13.49 per cent (low rate), August 2026
The Moneysmart mortgage and credit card calculators for checking, and a spreadsheet

How to do it

Record the RBA rates with their dates; use a loan of $600 000 over 30 years with monthly repayments as the test case.
Compute the monthly repayment M = P i (1 + i)^n / ((1 + i)^n - 1) with i = 0.062/12 and n = 360, and the total paid and interest paid.
Build the reducing balance table for the first three months: interest = balance x i, new balance = balance + interest - M.
Change the rate to the 8.77 per cent standard variable rate and compare repayments and total interest.
Add $200 to each monthly repayment, then instead pay half the monthly repayment every fortnight, and find the new term and interest saved.
For a credit card balance of $2000 left unpaid for 30 days, compute the daily-compounded interest at 20.99 and 13.49 per cent a year.

What you should see

At 6.2 per cent the repayment is $3674.81 a month; over 360 months the borrower pays $1 322 932.99, of which $722 932.99 is interest. With the repayment kept unrounded, as a spreadsheet keeps it, the first three months' interest is $3100.00, $3097.03 and $3094.04, leaving balances of $599 425.19, $598 847.40 and $598 266.63. At 8.77 per cent the repayment rises to $4728.78. Paying $200 extra each month clears the loan in 313 months (26.1 years) and saves $112 650.33; paying half the repayment each fortnight clears it in 634 fortnights (24.4 years) and saves $159 450.33. On the credit card, 30 days of daily compounding costs $34.79 at 20.99 per cent and $22.29 at 13.49 per cent. The learner knows it worked when the spreadsheet balance reaches zero at month 360 and the repayment matches the Moneysmart calculator.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

Half of each early repayment goes to the loan; in the first month $3100.00 of $3674.81 is interest.
A slightly higher rate adds a little to the cost; 8.77 per cent instead of 6.2 per cent adds $1053.97 a month.
Paying half the monthly amount each fortnight is the same as paying monthly; 26 half-payments a year equal 13 monthly repayments.

Safety card

Low riskLearners carry it out

Hazards

No hazard is listed.

Controls

No control is listed.

Note

No chemicals and no heat: the NSW Department of Education Chemical Safety in Schools package does not apply. The activity uses published rates and stated test amounts only; no learner's or family's own financial details are needed.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics Advanced 11–12 Syllabus (2024), Year 12 focus area Financial mathematics; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MAV-12-08
Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 2 focus area Investment and loans; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S2-02
Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 1 focus area Depreciation and loans; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S1-03
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

All Concept Studio activities