Module Review — Investment and Loans
You have now journeyed through the mathematics of money — from the simple linear growth of basic interest to the exponential power of compounding, from the steady accumulation of annuities to the careful management of loans and debt. This review lesson consolidates every concept, formula, and strategy from the module into a coherent framework. Use it to identify gaps, strengthen understanding, and prepare for your HSC examination.
Practise this lesson
Three printable worksheets that build from foundations to mastery — or build your own from any module’s questions.
From all 12 lessons in Module 7, which single concept do you think has the biggest real-life impact on your financial future? And which formula do you find hardest to remember? Write your answers before reviewing.
Before reading on — this is your self-assessment starting point.
Every HSC Module 7 question uses one or more of these formulas. Know them all.
Simple interest: $I = Prn$ and $A = P(1 + rn)$. Linear growth — interest does not compound.
Compound interest: $A = P(1 + r)^n$ or $A = P\left(1 + \frac{r}{k}\right)^{kn}$. Exponential growth — interest earns interest.
Effective annual rate: $\text{EAR} = \left(1 + \frac{r}{k}\right)^k - 1$. Converts nominal rate to true annual rate for fair comparison.
Key facts
- All six module formulas
- Common pitfalls and traps
- HSC exam technique tips
Concepts
- How all lessons interconnect
- When to use each formula
- Why flat rates are misleading
Skills
- Work through exam-style questions
- Compare options with full justification
- Identify and correct common errors
Lesson 1 — Simple Interest: Linear growth. $I = P \times r \times n$. Used for short-term loans and basic investments. Interest does not compound.
Lesson 2 — Compound Interest: Exponential growth. $A = P(1+r)^n$. Interest earns interest. More frequent compounding gives higher returns.
Lesson 3 — Comparing Rates: Convert to effective annual rates before comparing. Beware flat rate traps. Rule of 72 for quick estimates: doubling time $\approx 72/r$.
Lesson 4 — Annuities: Regular equal payments. Ordinary annuity (end of period) vs annuity due (start of period). FV and PV formulas.
Lesson 5 — Future Value: What regular savings become. Start early for dramatic effects. $FV = M[(1+r)^n - 1]/r$.
Lesson 6 — Present Value: What future payments are worth today. Foundation of all loan calculations. $PV = M[1-(1+r)^{-n}]/r$.
Lesson 7 — Loans and Amortisation: Repayment schedules. Early payments are mostly interest. Extra repayments save the most when made early in the loan term.
Lesson 8 — Reducing Balance Loans: Flat rate vs reducing balance. Flat rates disguise much higher true costs. Always ask which method is used.
Lesson 9 — Credit Cards: Daily interest, minimum payment traps, interest-free periods, balance transfers. Pay in full each month to avoid all interest.
Lesson 10 — Investment Strategies: Risk-return trade-off, diversification, real returns, time horizon. Match strategy to goals and risk tolerance.
Lesson 11 — Mixed Problems: Integrate multiple concepts. Systematic approach: identify, list, choose, calculate, compare.
What to write in your book
- Simple interest: linear. Compound interest: exponential. This difference matters enormously over long time periods.
- Annuities: FV is for savings (growing), PV is for loans (borrowing). Same payments, opposite direction.
- Flat rate true cost: $r_{\text{reducing}} \approx \frac{2n \cdot r_{\text{flat}}}{n+1}$ — roughly double the stated flat rate.
Quick check: Which formula would you use to find how large a $500/month investment grows to after 10 years at 6% p.a. compounded monthly?
These are the most common errors in Module 7 HSC responses:
What to write in your book
- Always convert: annual rate $\div$ periods per year = period rate. Years $\times$ periods per year = total $n$.
- Flat rate true cost $\approx$ double the stated flat rate in terms of equivalent reducing balance rate.
- Use EAR to compare rates with different compounding frequencies.
True or false: A 6% flat rate loan over 5 years has the same total cost as a 6% reducing balance loan over 5 years on the same principal.
- Show all working: method marks are awarded even if the final answer is wrong. A correct formula with a calculation error still earns marks.
- State formulas first: write the formula, then substitute values. This makes it easy for the marker to follow your reasoning.
- Define your variables: clearly state what $P$, $r$, $n$, $M$ represent in each specific question.
- Use correct units: dollars to 2 decimal places, percentages to 2 decimal places unless specified otherwise.
- Interpret your answers: for comparison questions, explicitly state which option is better and why — do not just calculate and stop.
- Check reasonableness: does your answer make sense? A $50,000 loan over 5 years should not produce $5 million in interest.
- Round only at the end: keep full precision throughout calculations, then round the final answer to avoid rounding errors accumulating.
What to write in your book
- Show formula → substitute → calculate → interpret. Four steps for every financial question.
- Round only the final answer. Use full precision for intermediate steps.
- State which option is better and why — one sentence of justification earns a mark.
Fill the gap: A $10,000 investment at 5.4% p.a. compounded quarterly for 6 years has $r = 0.054 \div 4 = 0.0135$ per quarter and $n = $ quarters.
Revision practice · 3 activities
Formula drills. Without looking at the reference, write all six Module 7 formulas from memory. Then check your answers against the formula summary card above.
Mixed practice. (a) Find the monthly repayment on a $250,000 mortgage at 4.8% p.a. compounded monthly over 25 years. Find total interest. (b) Compare the effective annual rates of 5.8% compounded monthly versus 6.0% compounded semi-annually. Which is better for an investor?
Exam-style. A person contributes $400/month to super from age 30 to 65 at 7% p.a. compounded monthly. Find the balance at 65. How much of that is interest earned (not contributions)?
Match each formula to its use:
Most students find the biggest real-life impact comes from compound interest and superannuation — starting early and using tax-advantaged vehicles creates enormous long-term wealth differences. The hardest formula is usually the loan repayment: $M = PV \cdot r / [1-(1+r)^{-n}]$ — remember it derives from the PV annuity formula rearranged for $M$.
What has changed in your understanding? What will you do differently as a result of this module?
Top 3 list: Name THREE specific HSC exam mistakes described in this lesson. For each, write one sentence explaining how to avoid it.
Pick your answer, then rate your confidence — that tells the system what to drill next.
Q1. A $10,000 investment at 5.4% p.a. compounded quarterly for 6 years. Which calculation gives the correct final value?
Q2. $300/month is invested at 6% p.a. compounded monthly for 20 years. What is $r$ in the FV formula?
Q3. A $15,000 car loan at 5.5% flat rate over 4 years. The total interest is:
Q4. Which effective annual rate is higher: 5.8% compounded monthly, or 6.0% compounded semi-annually?
Q5. On a reducing balance mortgage, which statement about early repayments is correct?
SA 1. (a) Calculate the future value of $250 monthly contributions at 5.4% p.a. compounded monthly for 8 years. (b) Find the present value of $800 monthly loan repayments for 4 years at 6% p.a. compounded monthly. (c) Compare the effective rates of 6.2% compounded monthly and 6.3% compounded quarterly. (2 marks)
SA 2. A $320,000 mortgage at 5.4% p.a. compounded monthly over 25 years. (a) Find the monthly repayment. (b) Find total interest. (c) After 5 years the rate drops to 4.8%. Find the new repayment for the remaining 20 years. (d) Calculate total interest saved by the rate drop. (2 marks)
SA 3. A 28-year-old earns $70,000 and receives 11.5% employer super contributions. They salary sacrifice an additional $400/month. The super fund earns 7.2% p.a. compounded monthly. (a) Calculate the total monthly super contribution. (b) Find the super balance at age 65. (c) If they instead took the $400 as after-tax income (32.5% marginal rate) and invested at 8% p.a. compounded monthly, what would the balance be at 65? (d) Calculate the difference and explain the superannuation advantage. (e) Identify one risk of having all retirement savings in superannuation. (3 marks)
Comprehensive answers (click to reveal)
MC 1 — B: Quarterly compounding: $r = 0.054/4 = 0.0135$; $n = 6 \times 4 = 24$. So $A = 10000 \times (1.0135)^{24}$.
MC 2 — C: $r = 0.06 / 12 = 0.005$ per month.
MC 3 — D: Flat rate interest = $15000 \times 0.055 \times 4 = \$3{,}300$.
MC 4 — C: Monthly EAR = $(1.00483...)^{12}-1 \approx 5.96\%$. Semi-annual EAR = $(1.03)^2 - 1 = 6.09\%$. Semi-annual 6% is higher.
MC 5 — B: Early repayments reduce the outstanding balance earliest, so interest is calculated on a smaller amount for more periods — saving is greatest when made early.
SA 1 (2 marks): (a) $29,625 [0.5]. (b) $34,064 [0.5]. (c) Correct EAR calculation and comparison [1].
SA 2 (2 marks): (a) $1949.37 [0.5]. (b) $264,811 [0.5]. (c) $1926.29 [0.5]. (d) $5,539 [0.5].
SA 3 (3 marks): (a) $1070.83 [0.5]. (b) $2,379,385 [0.5]. (c) $380,970 [0.5]. (d) Difference + tax explanation [1]. (e) Legislative/concentration risk [0.5].
Drill 2: Monthly repayment $\approx \$1{,}433.48$; Total $\approx \$430{,}044$; Interest $\approx \$180{,}044$. Monthly EAR 5.96%; Semi-annual EAR 6.09% — semi-annual is better for investor.
Drill 3: $FV = 400 \times [(1.005833)^{420}-1]/0.005833 \approx \$1{,}499{,}569$. Contributed $= 400 \times 420 = \$168{,}000$. Interest earned $\approx \$1{,}331{,}569$.
Five timed questions covering the full breadth of Module 7 — simple interest, compound interest, effective rates, annuities, and loan comparisons. Beat the boss to bank a tier — gold (90% + speed), silver (75%), or bronze (50%). Replays welcome.
⚔ Enter the arenaClimb platforms using all Module 7 review concepts. Pool: lesson 12.
Module 7 Complete!
You have completed all 12 lessons of Investment and Loans.
Outcomes covered: MS-F4 — applies financial mathematics to solve problems in real-world contexts including investments, loans and superannuation.
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