Integrate simple interest, compound interest and depreciation in HSC-style multi-part problems — including loan comparisons, investment decisions and mixed extended response questions.
Use the PDF for classwork, homework or revision. It includes key ideas, activities, questions, an extend task and success-criteria proof.
Interest and depreciation questions in the HSC love to combine multiple concepts in a single scenario. A business might borrow money at compound interest to buy equipment that depreciates — and you could be asked about both in the same question. Or an investment question might compare simple versus compound interest, then ask which option a rational person should choose and why. The mathematics is never harder than what you've already practised — the challenge is recognising which formula to use, in what order, and making sure your answer actually responds to the question being asked. Before you start: if you had $10,000 to invest for 5 years, what would you want to know before choosing a product?
Identify which formula applies from the language used in each question part
Compare investment and loan options, stating which is better and by how much
Find unknown depreciation rates by rearranging $S = V_0(1-r)^n$
Maximise marks in extended response questions by labelling steps and showing $(1 \pm r)^n$ explicitly
Wrong: Straight-line and declining-balance depreciation give the same result each year.
Right: Straight-line deducts a constant dollar amount each year. Declining-balance deducts a constant percentage of the current value, so the dollar amount decreases over time.
The first step in any Interest and Depreciation question is identifying which formula applies — and the signal is always in how the rate is described.
| Question says… | Use this formula |
|---|---|
| "simple interest", "flat rate", "interest on the principal only" | I = Prn |
| "compound interest", "compounds annually/monthly", "interest on the balance" | A = P(1+r)^n |
| "straight-line", "fixed amount per year", gives a dollar depreciation figure | S = V₀ − Dn |
| "declining balance", "reducing balance", "depreciates at X% per annum" | S = V₀(1−r)^n |
Comparison questions require calculating a quantity under two different conditions and identifying which is better — for an investor, higher final amount is better; for a borrower, lower total repayment is better.
The most common comparison formats:
For all comparisons: use identical time periods, calculate both fully, state a conclusion with the dollar difference, and identify who benefits.
In 4–6 mark extended response questions, the marks are distributed across method steps — showing every step of every formula application is essential.
Recommended layout for any Interest or Depreciation calculation:
A student who makes one arithmetic error but carries it forward correctly can still score 4 out of 5. The mark is for the method, not just the number. A marker cannot award marks for working they cannot find.
In capstone questions, the biggest challenge is not the algebra itself but deciding the order of attack, especially when one result feeds into the next part.
| Question type | Best order |
|---|---|
| Loan comparison | Calculate both totals fully, then compare borrower cost |
| Investment choice | Find final amount for each option, then identify the larger return |
| Depreciation and resale | Find salvage value first, then total depreciation or difference |
| Mixed asset vs investment | Find the depreciated value and the invested value separately before comparing |
| Unknown rate question | Write the model first, isolate the power expression second, solve for the rate last |
Aiko needs to borrow $18,000 for 3 years. Lender A offers simple interest at 7.5% per annum. Lender B offers compound interest at 6.8% per annum compounding annually. (a) Calculate the total amount repaid under each lender. (b) Which lender should Aiko choose, and by how much is it cheaper?
$P = \$18{,}000$, $r = 0.075$, $n = 3$
$$I = Prn = \$18{,}000 \times 0.075 \times 3 = \$4{,}050.00$$
$$\therefore \text{Total repaid (A)} = \$18{,}000 + \$4{,}050 = \$22{,}050.00$$
Simple interest: flat rate applied to the original principal for 3 years.
A business spends $28,000 on a new machine. The machine depreciates at 15% per annum declining balance. Simultaneously, the business invests $28,000 in a term deposit earning 4.2% per annum compounding semi-annually. (a) What is the machine's value after 4 years? (b) What is the investment worth after 4 years? (c) What is the difference between the investment value and the machine's value?
$V_0 = \$28{,}000$, $r = 0.15$, $(1-r) = 0.85$, $n = 4$
$$(0.85)^4 = 0.52201\ldots \quad \text{(calculator)}$$
$$\therefore S = \$28{,}000 \times 0.52201 = \$14{,}616.28$$
Apply declining balance formula. The machine has lost almost half its value in 4 years at 15% per annum.
A boat purchased for $54,000 has a salvage value of $29,160 after 4 years of declining balance depreciation. Find the annual depreciation rate.
Start from $S = V_0(1-r)^n$:
$$\$29{,}160 = \$54{,}000 \times (1-r)^4$$
Substitute the known values — $S = \$29{,}160$, $V_0 = \$54{,}000$, $n = 4$. Solve for $r$.
Nina has $12,000 to invest for 4 years. Product A offers 5.1% per annum compounding annually. Product B offers 4.9% per annum compounding monthly.
Which product gives the larger final amount, and by how much?
$$A_A = \$12{,}000(1.051)^4$$
$$A_A = \$12{,}000 \times 1.220199800\ldots = \$14{,}642.40$$
Annual compounding uses the annual rate directly, with $n = 4$ periods.
Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?
5 random questions from a replayable lesson bank — feedback shown immediately
A machine costs $60,000 and depreciates by $5,500 per year (straight-line). After how many complete years will its value first fall below $20,000?
A car purchased for $42,000 depreciates at 20% per annum declining balance. What is its value after 3 years?
$18,000 is invested at 4.8% per annum compounding quarterly for 2 years. What is the final amount?
These are final capstone-style questions designed to practise identifying the model quickly and finishing with a proper conclusion sentence.
A savings account invests $14,500 at 5.3% per annum compounding annually for 3 years. Calculate the final amount and the interest earned.
A business buys equipment for $36,000. It depreciates at 18% per annum declining balance. Find its value after 5 years and the total depreciation.
Compare two investment options for $20,000 over 4 years: Option A is simple interest at 6.1% per annum; Option B is compound interest at 5.7% per annum compounding annually. Which option is better?
Use this as a last recognition drill for the whole module: identify the model first, then decide the direction of the comparison.
Which wording most strongly signals compound interest?
For a borrower comparing two loans, which outcome is better?
What should be shown as a separate line in many compound-interest and depreciation questions to preserve method marks?
If an asset depreciates at 14% per annum declining balance, what expression should appear in the formula?
You've worked through all 14 lessons covering Earning Money, Managing Money, and Interest & Depreciation — the full MS-F1 Financial Mathematics syllabus.
Test your knowledge with the checkpoint quizzes and module topic test.