Module Review, Investment and Loans

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.

Module 7 covers: simple interest (I = Prn), compound interest (A = P(1+r)^n), depreciation (straight-line S = V₀ − Dn; declining balance S = V₀(1−r)^n), annuities (FV and PV formulas), and loan comparison methods.

Pause, copy all five formula families: I = Prn (simple interest), A = P(1+r)^n (compound growth), S = V₀ − Dn (straight-line depreciation), S = V₀(1−r)^n (declining balance), and FV/PV annuity formulas, as a one-page quick-reference into your book.

The module covers five formula families: I = Prn (simple interest), A = P(1+r)^n (compound), S = V₀ − Dn and S = V₀(1−r)^n (depreciation), and the FV/PV annuity formulas. Four errors appear in almost every HSC paper: using the annual rate without dividing by compounding frequency, confusing n (total periods) with years, calculating A instead of I (or vice versa), and rounding intermediate values too early.

These are the most common errors in Module 7 HSC responses:

Common HSC errors in financial maths: using annual rate without dividing by compounding frequency; confusing n (periods) with years; forgetting to subtract principal when the question asks for interest only; rounding intermediate steps.

Pause, copy the four HSC errors and fixes: (1) rate not divided by k → always convert annual rate to per-period; (2) n in years not periods → multiply years by k; (3) returning A when I is asked → I = A − P; (4) rounding too early → keep full precision until the last step into your book.

• 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.

Knowing the four pitfalls, unscaled rate, wrong n, total vs interest confusion, premature rounding, prevents most mark losses. To also maximise method marks (awarded even if the final number is wrong), use the four-step technique: write the formula first, list all variable values clearly, substitute, then round only the final answer to two decimal places for money.

HSC technique for financial maths: write down the formula first, list all known values with units, substitute clearly, and express answers to two decimal places for money. In multi-part questions, carry full-precision values between steps.

Pause, copy the four-step technique: (1) write the formula; (2) list all known values with units; (3) substitute clearly; (4) express money answers to two decimal places only at the final step, this structure earns method marks even when the answer is wrong into your book.