Managing Money

Managing money is about buying things sensibly and keeping a budget. It was not examined on its own in NESA's sample HSC paper, but its percentage skills appear all through Investment and loans and Annuities in Year 12, and a practical budgeting or purchase question can appear in any HSC paper.

• Percentages: increase, decrease, mark-ups and discounts, and percentage change.
• GST in Australia and VAT overseas; converting between currencies.
• Payment options: cash, credit cards, buy now pay later, and buying on terms with a deposit and repayments.
• Comparing costs of different ways to pay and justifying the best choice.
• Vehicles: the purchase price or loan repayments, stamp duty, registration, insurance, and the ongoing running costs.
• Household bills for electricity, gas and water.
• Budgets: fixed and discretionary spending, saving, an emergency fund of 3 to 6 months of living expenses.

To increase an amount by $r\%$, multiply by $1+\frac{r}{100}$. To decrease it by $r\%$, multiply by $1-\frac{r}{100}$.

• A mark-up is the amount a seller adds to the cost price to set the selling price.
• A discount is an amount taken off the marked price.
• Percentage change compares the change with the original amount.

For example, a price rising from $40 to $46 is a change of $6, which is $\frac{6}{40}\times 100=15\%$ of the original price.

Worked example: mark-up then discount

A shop buys a jacket for $80 and marks it up by 45%. In a sale, the marked price is reduced by 20%. Find the sale price.

The sale price is $92.80. Notice that a 45% increase followed by a 20% decrease is not a 25% increase overall ($80\times 1.25=100$), because the 20% is taken from the bigger amount.

The Goods and Services Tax (GST) in Australia is 10% of the pre-GST price. Many countries have a similar tax called VAT (value added tax), at different rates.

• To add GST, multiply the pre-GST price by 1.1.
• If a price includes GST, the GST is one-eleventh of it: divide by 11.
• The pre-GST price is the GST-inclusive price divided by 1.1.

For example, a bill of $264 including GST contains $264÷11=24$ dollars of GST, and the pre-GST price is $240. Taking 10% of $264 ($26.40) is wrong, because the 10% is of the pre-GST price, not the total.

To convert currency, multiply or divide by the exchange rate. If $1 AUD buys 0.65 USD, then a US$240 item costs $240÷0.65=369.23$ Australian dollars. Check that the answer makes sense: Australian dollars are worth less than US dollars at this rate, so you need more of them.

• Cash or debit card: no extra cost, but you need the money now.
• Credit card: usually an interest-free period; interest is charged on any amount not paid by the due date, often at a high rate.
• Buy now pay later (BNPL): the price is split into a few instalments; there is usually no interest, but missed payments attract late fees, and some plans charge account fees.
• Buying on terms: pay a deposit and then regular repayments. The total is usually more than the cash price; the difference is the interest charged.

Worked example: cash or terms

A television has a cash price of $1899. It can also be bought on terms with a 15% deposit and 24 monthly repayments of $75. Find the total cost on terms, and how much more this is than the cash price as a percentage.

Buying on terms costs $2084.85, which is $185.85 or about 9.8% more than paying cash. When asked to justify the best method, compare the totals and also consider the situation: terms may suit someone who needs the item now and can't pay all at once, as long as they can make every repayment.

The cost of buying a car is more than the price on the windscreen:

• Purchase price, or the total of loan repayments if the car is bought with a loan.
• Stamp duty, a state tax on the purchase. In a question it is usually given as a rate, such as $3 for every $100 or part of $100 of the price.
• Registration, which in NSW requires compulsory third party (CTP) insurance first (the green slip, bought separately from an insurer), covering injury to people.
• Non-compulsory insurance: third-party property (damage to other people's property) or comprehensive (also covers your own car).

Example. For a car costing $28 450 with stamp duty of $3 per $100 or part of $100: $28450÷100=284.5$, and the "or part" rounds this up to 285 lots of $100. The duty is $285\times 3=855$ dollars. In NSW this is the actual rate for cars up to $45 000; above that it is $1350 plus $5 per $100 or part over $45 000.

Ongoing running costs include fuel, servicing, tyres, repairs, registration and insurance each year, and depreciation (the loss of value over time). Fuel cost uses the car's fuel consumption in L/100 km. A spreadsheet is a good way to total all these costs over a year.

Electricity and gas are charged per unit used (kilowatt hours or megajoules) plus a daily supply charge. Water is charged per kilolitre plus a fixed service charge. Find the usage from the meter readings (end minus start), multiply by the rate, and add the fixed charges.

Example. A household used 48 kL of water in a quarter. Water costs $2.67 per kL and the service charge is $47.50 per quarter. The bill is $48\times 2.67+47.50=175.66$, so $175.66. Watch for rates in cents: 28 c/kWh is $0.28 per kWh.

A budget plans income and spending over a period. Start from net (take-home) income.

• Fixed expenses stay the same each period: rent, loan repayments, insurance, phone plan.
• Variable or discretionary expenses change or are optional: food, entertainment, clothes, eating out.
• Income minus expenses is what is left to save.

Good strategies to avoid money problems are budgeting, saving regularly, monitoring spending, and building an emergency fund of 3 to 6 months of living expenses for events like losing a job or a large repair bill. For someone whose essential expenses are $2350 per month, that is between $3\times 2350=7050$ and $6\times 2350=14100$ dollars.

Make sure all items are in the same period before adding them. Change weekly costs to monthly by multiplying by 52 and dividing by 12, not by multiplying by 4.

• Finding GST on a GST-inclusive price by taking 10% of it. Divide by 11.
• Adding and subtracting percentages, such as treating +45% then −20% as +25%.
• Calculating percentage change using the new amount as the denominator.
• Forgetting the deposit when finding the total cost on terms.
• Not rounding up for "or part of $100" in stamp duty.
• Mixing weekly, fortnightly and monthly amounts in one budget.

• Justify or compare questions need numbers for each option and a conclusion that names the better choice and gives a reason.
• Write money to the nearest cent, with a dollar sign in your final sentence.
• Show the meter reading subtraction in bill questions; it often earns its own mark.
• Read the conditions of a BNPL or credit plan carefully: when fees apply, and whether interest is charged from the purchase date or after the interest-free period.

• Earning money: net pay is the starting point for a budget.
• Investment and loans (Year 12): depreciation, compound interest, credit cards and reducing-balance loans extend the percentage skills here.
• Ratios and rates (Year 12): fuel consumption and energy use are rates.
• Formulas and equations: substituting into cost formulas.