Buying on terms and buy now, pay later schemes for HSC Maths Standard 2: total cost, finance charges, flat interest rates and fees (Year 11 Managing money, 2024 syllabus)

Syllabus dot point

“Calculate the cost of buying on terms with an initial deposit and regular repayments, examine payment options such as buy now, pay later schemes and analyse the costs of each, and justify the best method of purchase for a given context”

10 min readUpdated 7 Oct 2026

Quick answer

Total paid on terms is the deposit plus all the payments, and the finance charge is the total minus the cash price. A flat interest rate is $r = \frac{I}{Pn}$ on the amount borrowed (price minus deposit) with $n$ in years. Buy now, pay later plans may have no interest but can have fees, so compare total costs and say which option suits the buyer. Part of Year 11 Managing money in the 2024 Mathematics Standard syllabus.

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What this dot point is asking
The answer
Practice questions

What this dot point is asking

In the Mathematics Standard 11-12 Syllabus (2024), first examined in the 2027 HSC, the Year 11 focus area Managing money asks you to "calculate the cost of buying on terms" with an initial deposit and regular repayments, to examine payment options involving "buy now, pay later" schemes and analyse the costs, and to compare the total cost of different methods and justify which suits a context. Buy now, pay later schemes are new to the Standard syllabus. Year 11 is assumed knowledge in the Year 12 HSC.

Note

Buying on terms is paying for something in pieces. You pay part now (the deposit), then regular payments, and the seller adds a charge for the wait. The shop's price on the tag is smaller than the total of all your payments. Your job is to add up what you really pay and compare it with the cash price.

The answer

Key fact

\text{total paid} = \text{deposit} + (\text{number of payments} \times \text{payment})

\text{extra cost (finance charge)} = \text{total paid} - \text{cash price}

\text{amount borrowed} = \text{cash price} - \text{deposit}

The flat interest rate treats the charge as simple interest on the amount borrowed: $I = Prn$ , so $r = \frac{I}{Pn}$ with $n$ in years.

Buying on terms, step by step

Take a $960 balance after a deposit, repaid by $24$ payments of $45.50.

Total of the payments: $24 \times 45.50 = \$1092$ .
Finance charge: $1092 - 960 = \$132$ .
Flat rate over $2$ years: $\frac{132}{960 \times 2} = 6.875\%$ per year, which is $6.88\%$ to two decimal places.

Rounding rule used on this page: money is to the nearest cent and rates are to two decimal places, rounded only at the end.

A flat rate is a convenient comparison, but it is not the true rate. The balance owed falls with each payment, yet the charge is calculated on the whole amount borrowed, so the effective rate is higher than the flat rate.

Buy now, pay later schemes

A buy now, pay later plan lets you take the goods straight away and pay in a few equal instalments, often fortnightly. Many advertise no interest. The costs to look for are:

Fees: late payment fees, account fees or fees per missed payment (the questions on this page use made-up fees; always read the real terms).
Overlap: several plans at once can take a large share of your income in one pay period.
Temptation: instalments look small, so it is easy to buy more than you planned.

To compare two options, work out the total you pay for each in the situation described (including any fee a missed payment would trigger), then choose the lowest total that you can actually afford. Cash is not available to everyone, so the question may ask you to justify a method for a particular buyer.

Worked examples

Total and extra cost

A $1200 television with a $20\%$ deposit ($240) and $24$ payments of $45.50 costs $240 + 1092 = \$1332$ , which is $132 more than cash.

Marker's note: show the deposit, the payments total and the subtraction as separate lines.

A BNPL plan with a late fee

A $360 purchase in $4$ equal instalments is $90 each. One late fee of $10 makes the total $370.

Marker's note: "no interest" does not mean "no extra cost" once fees apply.

Comparing three methods

A $1800 laptop costs $1710 cash on the day, $1980 on terms ($180 deposit plus $12 \times \$150$ ) or $1800 by BNPL if every instalment is paid on time. Cash is cheapest. Terms cost $270 more than cash.

Marker's note: finish with the comparison and a named conclusion.

Common traps

Forgetting the deposit in the total: The deposit is part of what you pay.
Using the cash price as the amount borrowed: The deposit reduces the amount borrowed, so the flat rate uses price minus deposit.
Using months as years: In $r = \frac{I}{Pn}$ the term must be in years: $24$ months is $2$ years.
Ignoring fees: Compare the total including any fee a missed payment would trigger.
Choosing the cheapest without reading the context: If the buyer cannot pay cash, justify the cheapest option they can afford.

Exam technique

Lay out three lines: total paid, extra cost, then the comparison or rate. Write the units in dollars and percentages, and finish "compare" questions with a one-line decision that names the option and the dollar difference. Keep the numbers unrounded until the last line.

Practice questions

Original practice questions graded from foundation to exam level, each with a full worked solution. Try them before revealing the solution.

foundation3 marks

A television has a cash price of $1200. It can be bought on terms with a

20\%

deposit and

24

monthly payments of $45.50. Find the deposit, the total paid and the extra cost of buying on terms.

Show worked solution →

Deposit: $20\% \times 1200 = \$240$ .
Total paid: $240 + 24 \times 45.50 = 240 + 1092 = \$1332$ .
Extra cost: $1332 - 1200 = \$132$ .

Marker's note: one mark for each of the three values. The extra cost is the total paid minus the cash price.

foundation2 marks

A $360 jacket is bought through a buy now, pay later plan with

4

equal fortnightly instalments and no interest. Each missed instalment costs a late fee of $10. Find the instalment, and the total paid if one instalment is paid late.

Show worked solution →

Instalment. $\frac{360}{4} = \$90$ .

One late payment. $360 + 10 = \$370$ .

Marker's note: one mark for each answer. A plan with no interest can still cost more than the price if fees are charged.

core3 marks

For the television in the first question, the amount borrowed is the cash price less the deposit. Find the amount borrowed, the finance charge and the equivalent flat interest rate per year, as a percentage to two decimal places. (Use

I = Prn

with

P

the amount borrowed and

n

in years.)

Show worked solution →

Amount borrowed: $1200 - 240 = \$960$ .
Finance charge: The payments total $24 \times 45.50 = \$1092$ , so the charge is $1092 - 960 = \$132$ .
Flat rate: The term is $2$ years, so

132 = 960 \times r \times 2 \quad\Rightarrow\quad r = \frac{132}{1920} = 0.06875 \approx 6.88\% \text{ per year}.

Marker's note: one mark for $\$960$ , one for $\$132$ , one for $6.88\%$ . A flat rate understates the true cost, because the balance owed falls as you pay but the charge is worked on the full amount borrowed.

core4 marks

A laptop costs $1800 cash, or $1710 if paid in full on the day (a

5\%

discount). Other options are: terms with a $180 deposit and

12

monthly payments of $150; or a buy now, pay later plan with

4

equal fortnightly instalments, which costs a $10 late fee if one instalment is missed. Assume every payment is made on time. Find the cheapest way to pay, and how much more the terms option costs than that.

Show worked solution →

Pay in full on the day: $0.95 \times 1800 = \$1710$ .
Terms: $180 + 12 \times 150 = 180 + 1800 = \$1980$ .
Buy now, pay later, no missed payment: The instalments total $1800.
Compare: The cheapest is the discounted cash price of $1710. Terms costs $1980 - 1710 = \$270$ more.

Marker's note: one mark for each of the three totals, and one for naming the cheapest option and the $270 difference. Costs are not the only factor: a buyer without $1710 saved cannot use the cash option.

exam4 marks

A sofa is advertised at $2400. On terms it requires a $300 deposit and

36

monthly payments of $68.75. (a) Find the total paid and the finance charge. (b) Find the equivalent flat interest rate per year, as a percentage to two decimal places, on the amount borrowed. (c) The shop offers the same sofa on a credit plan at a flat

8\%

per year, with the same deposit and term. Which plan has the lower rate?

Show worked solution →

(a) Total and charge. The payments total $36 \times 68.75 = \$2475$ , so the total paid is $300 + 2475 = \$2775$ . The amount borrowed is $2400 - 300 = \$2100$ , so the finance charge is $2475 - 2100 = \$375$ (also $2775 - 2400$ ).

(b) Flat rate. The term is $3$ years:

r = \frac{375}{2100 \times 3} = 0.0595\ldots \approx 5.95\% \text{ per year}.

(c) Compare. $5.95\% < 8\%$ , so the terms offer has the lower flat rate.

Marker's note: one mark for the total, one for $375, one for $5.95\%$ , one for the comparison with a reason.

exam4 marks

Priya buys three items from three different buy now, pay later providers. Each plan has

4

fortnightly instalments of $62.50, and the first instalments are all due in the same fortnight. Her net pay is $1850 per fortnight. (a) Find the total she must pay in that fortnight, and the percentage of her net pay it takes, to one decimal place. (b) Find the total she will owe across the three plans over the

4

fortnights. (c) Give one reason this could be a financial risk.

Show worked solution →

(a) One fortnight: $3 \times 62.50 = \$187.50$ . As a percentage of net pay, $\frac{187.50}{1850} \times 100 = 10.135\ldots \approx 10.1\%$ .
(b) Total owed: $3 \times 4 \times 62.50 = \$750$ .
(c) Risk: Overlapping plans can use a noticeable part of income before rent and bills are paid, and if a payment is missed a late fee may be charged, so small instalments can add up and make budgeting harder.

Marker's note: one mark for each of (a) and (b), one for the percentage rounding, one for a sensible risk linked to the numbers.

Practise this

Sources & how we know this

Mathematics Standard 11-12 Syllabus (2024): Year 11 Managing money — NESA (2024)
Mathematics Standard Stage 6 Syllabus (2017) — NESA
Mathematics Standard HSC exam papers — NESA