How the problems are made
Every person, loan and asset is invented. Interest rates are chosen so the rate per period is an exact decimal, like 0.35% a month, and every answer is worked exactly and rounded once, to the cent, where the question says. Recurrence steps and amortisation rows are each worked from the rounded figure before them, as VCAA's reports do. HSC table questions use only the interest factors printed in the question. Topics run from one-step questions to exam-style problems in three parts.
An example from set MNA234
Zara borrows $53 000 at 6% per annum, compounding monthly, with 60 monthly repayments of $1024.64 except the last. If the last repayment were also $1024.64, it would overpay the loan by $0.11, so the final repayment is 1024.64 − 0.11 = $1024.53. Subtract it here: VCAA's 2023 report notes students who added the future value instead. Zara repays 59 × 1024.64 + 1024.53 = $61 478.29 in all, and the interest is 61 478.29 − 53 000 = $8478.29. On a finance solver: N = 60, I% = 6, PV = 53 000, PMT = −1024.64, FV = 0.11, P/Y = C/Y = 12. Open set MNA234
What each course asks for
VCE General Mathematics (Units 3 and 4, Recursion and financial modelling) models every balance with Vn+1 = R × Vn + d, reads amortisation tables and uses a finance solver. Money is given to the nearest cent with two decimals: VCAA's 2024 Exam 2 report says “$297 477.4 is not correct to the nearest cent”. When a table is given, VCAA's 2025 Exam 2 report says to use its values, as a finance solver gave a different balance.
HSC Mathematics Standard 2 works annuities from tables of future and present value interest factors, not from a formula. The 2024 syllabus, first examined in 2027, keeps this: “Calculations of annuities should be performed using a table of interest factors.” Loans use spreadsheets with interest rounded to the cent each month, or tables of monthly repayments per $1000 borrowed. Credit card interest compounds daily, counted from the day after the interest-free period up to and including the day of payment.
Questions
How do you complete a row of an amortisation table?
Multiply the balance after the previous payment by the interest rate per period (the annual rate divided by the number of payments a year) and round to the cent. The principal reduction is the payment minus that interest, and the new balance is the old balance minus the principal reduction. Work each row from the rounded figures in the row above.
Why does a finance solver give a different balance from the table?
A finance solver keeps every decimal, while an amortisation table rounds the interest to the cent in each row, so after a few rows the two can differ by a cent or more. VCAA's 2025 Examination 2 report says students were told to use the values in the table, and a solver's balance was not appropriate.
How do you find the final repayment of a loan?
Multiply the balance owing after the second-last repayment by R, which adds one more period's interest. Or, if a finance solver shows a small future value after the full number of regular repayments, adjust the regular repayment by it: add it when money is still owing, subtract it when the loan is overpaid. VCAA's 2023 report notes that some students added the $0.14 instead of subtracting it.
When do you multiply and when do you divide by an interest factor?
Write it as value = payment × factor. If the question gives the payment and asks for the future or present value, multiply. If it gives the value and asks for the payment, divide. NESA's 2023 and 2024 marking feedback lists knowing when to divide by the factor and when to multiply as something to improve.
Can I use the annuity formula instead of the table in HSC Standard 2?
When a table is given, use it. NESA's 2024 marking feedback says that if a question has a table provided, the solution requires the table, and the 2024 syllabus says annuities are calculated with a table of interest factors. A formula can also give a slightly different answer from a factor printed to 3 or 4 decimal places.
How do you count the days of credit card interest?
Count the date of purchase as day 1. Interest is charged from the day after the interest-free period up to and including the day the account is paid, so the days charged are the payment's day number minus the interest-free days. Then A = P(1 + r ÷ 365)^n, and the interest is A minus the purchase.
What is the difference between the nominal and effective interest rate?
The nominal rate is the quoted annual rate. The effective rate is the interest actually earned in a year once compounding is counted: ((1 + r ÷ (100 × k))^k − 1) × 100%, where k is the number of compounding periods a year. So 6% per annum compounding monthly is 6.17% effective.
Sources, checked 28 October 2026: VCAA VCE Mathematics Study Design, from 2023 (Word); VCAA General Mathematics past examinations and reports, including the 2023, 2024 and 2025 Examination 2 reports (Word); NESA HSC Mathematics Standard 2 papers, marking guidelines and marking feedback for 2023, 2024 and 2025; NSW Mathematics Standard 11–12 Syllabus (2024), content and teaching advice.