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NSWMaths Standard 2Quick questions
Year 12: Financial Mathematics
Quick questions on Reducing-balance loans, amortisation tables and total interest for HSC Maths Standard 2
12short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is how a reducing-balance loan works?Show answer
A loan of dollars is repaid by equal payments at the end of each compounding period. Each period:
What is amortisation table?Show answer
A standard format for the first few periods:
What is closed-form for the balance?Show answer
Iterating the recurrence using a geometric series gives
What is interest vs principal split?Show answer
Early in the loan, most of each payment goes to interest. Near the end, almost all goes to principal. This is why making extra repayments early saves a lot more interest than the same dollar amount later.
What is total interest paid?Show answer
If the loan is repaid by payments of :
What is australian mortgage context?Show answer
A typical Sydney mortgage in 2025: \7000006.2\%\sim 4.35\%25$ years monthly:
What is balance after many periods (closed form)?Show answer
For the same loan after years ():
What is australian mortgage (2025 rates)?Show answer
\6500006.0\%30$ years.
What is forgetting to convert the rate?Show answer
Monthly compounding requires the monthly rate . Using the annual rate gives a wildly wrong answer.
What is wrong sign on the closed form?Show answer
The balance formula subtracts the payment term. Sign errors mean you compute the wrong direction.
What is treating principal repaid as linear?Show answer
Early payments are mostly interest. The principal repayment grows geometrically each period.
What is ignoring the no-completion case?Show answer
If , the loan never finishes because the payment does not even cover the interest. A worded problem may test this. :::