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hscscience Maths Std · Y11
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Module 3 · L12 of 14 ~50 min MST-11-04 ⚡ +90 XP available

Buying on Terms, Buy Now Pay Later, and Comparing Purchase Methods

"No interest ever" is not the same as "no extra cost". Learn to total up what a deposit and a run of repayments really comes to, find the fees hiding inside a buy now pay later plan, then put the methods side by side and justify which one actually suits the person doing the buying.

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Think First

A checkout offers you a $\$480$ pair of headphones as "4 easy payments of $\$120$, 0% interest". Four times $\$120$ is exactly $\$480$, so the plan charges you nothing extra. Is that true? Write down what you think before you calculate, and note anything the advertisement has not told you.

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Learning Intentions

Calculate the total cost of buying on terms from a deposit and a run of regular repayments
Find the extra paid above the cash price, in dollars and as a percentage of the cash price
Analyse the account fees and late fees that make a buy now pay later plan cost more than the ticket price
Compare the total cost of paying cash, buying on terms, and using buy now pay later
Justify which purchasing method is best suited to a given person and situation, not just which is cheapest
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Key Terms

Cash priceThe single amount you would pay to walk out with the item today, with no plan attached. Like this: a fridge is ticketed at $\$1{,}200$, so the cash price is $\$1{,}200$ and every other method is measured against it.
DepositA first payment made up front, usually a set percentage of the cash price, before the repayments start. Like this: a 15% deposit on that $\$1{,}200$ fridge is $1200 \times 0.15 = \$180$ handed over on the day.
Buying on termsPaying a deposit and then fixed regular repayments until the item is paid off, with the extra cost built into the repayments. Like this: $\$180$ down and 24 monthly repayments of $\$52$ comes to $180 + 24 \times 52 = \$1{,}428$ in total.
Buy now pay later (BNPL)A plan that splits the ticket price into equal instalments and charges no interest, but does charge account fees and late fees. Like this: $\$480$ split into 4 fortnightly payments of $\$120$ costs $\$480$ in instalments plus whatever the account fee adds.
Account feeA small charge the BNPL provider adds every month the plan is open, whether or not you miss a payment. Like this: $\$6$ a month over the 2 months the plan runs adds $\$12$, so a $\$480$ purchase actually costs $\$492$.
Late feeA one-off charge added each time a scheduled payment is missed, on top of the account fee. Like this: missing one $\$120$ instalment on a plan with a $\$10$ late fee pushes the $\$492$ total to $\$502$.
Total costEvery dollar that leaves your hand under a method, added up, which is the only fair basis for comparing plans. Like this: deposit plus all repayments for terms, or instalments plus all fees for BNPL.
A bike has a cash price of $\$900$. On terms it is $\$180$ deposit and 12 monthly repayments of $\$68$. What is the total cost of buying on terms?
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Buying On Terms: Deposit Plus Repayments

Buying on terms means you take the item home today, hand over a deposit, and then make fixed repayments until it is paid off.

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Buying On Terms: Deposit Plus Repayments

Buying on terms means you take the item home today, hand over a deposit, and then make fixed repayments until it is paid off. The seller is carrying the risk of waiting for the money, and they charge you for that. The charge is not shown as an interest rate, it is baked into the repayments, so the only way to see it is to add everything up.

Two steps, every time:

  • Total cost $=$ deposit $+$ (repayment $\times$ number of repayments)
  • Extra paid $=$ total cost $-$ cash price

Take a fridge with a cash price of $\$1{,}200$, offered on terms as a 15% deposit and 24 monthly repayments of $\$52$.

The deposit is $1200 \times 0.15 = \$180$. The repayments come to $24 \times 52 = \$1{,}248$. So the total cost is $180 + 1248 = \$1{,}428$, and the extra paid is $1428 - 1200 = \$228$.

That $\$228$ is worth turning into a percentage of the cash price, because it is the number that lets you compare one deal against another: $\dfrac{228}{1200} \times 100 = 19\%$. The fridge cost 19% more than the ticket said.

Must do: Count the repayments carefully. "Two years of monthly repayments" is 24 payments, and "three years of fortnightly repayments" is 78, not 36.
Common error: Dividing the extra paid by the total cost instead of the cash price. Here that gives $228 \div 1428 = 16.0\%$, which understates the deal. The cash price is the thing you are comparing against, so it goes on the bottom.

Buying on terms: total cost = deposit + (repayment x number of repayments). Extra paid = total cost − cash price. Extra as a percentage = extra / cash price x 100. Fridge: 180 + 24 x 52 = 1428, extra 228, which is 19% of 1200 (dollars).

Pause, copy the two terms formulas into your book with the fridge worked beside them: deposit 180, repayments 24 × 52 = 1248, total 1428, extra 228, and 228 ÷ 1200 × 100 = 19%.

A $\$480$ purchase is paid through BNPL in 4 fortnightly instalments of $\$120$, with a $\$6$ monthly account fee over the 2 months the plan runs. The total paid is $\$$, which is % more than the ticket price.
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Buy Now Pay Later: Where The Cost Hides

BNPL splits the ticket price into equal instalments, usually fortnightly, and genuinely charges no interest.

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Buy Now Pay Later: Where The Cost Hides

BNPL splits the ticket price into equal instalments, usually fortnightly, and genuinely charges no interest. The instalments always add back up to exactly the purchase price. That is why the advertisement can say 0%, and it is true.

The cost is somewhere else. There are two charges to hunt for:

  • Account fee: charged every month the plan is open, whether or not anything goes wrong.
  • Late fee: charged each time a scheduled payment is missed.

So total cost = purchase price + account fees + late fees.

Return to the headphones from Think First: $\$480$, paid as 4 fortnightly instalments of $\$120$, with a $\$6$ monthly account fee. Four fortnights is 2 months, so the fees are $6 \times 2 = \$12$ and the total is $480 + 12 = \$492$. The extra is $\dfrac{12}{480} \times 100 = 2.5\%$ of the purchase price.

Now suppose one instalment is missed and the provider charges a $\$10$ late fee. The total becomes $492 + 10 = \$502$, and the extra paid is $\$22$, or $\dfrac{22}{480} \times 100 = 4.6\%$ (to one decimal place). One missed payment nearly doubled the cost of the plan.

Must do: Convert the instalment schedule into months before applying a monthly account fee. Four fortnightly payments run for 2 months, not 4.
Common error: Reading "0% interest" as "no extra cost" and answering that the plan costs the ticket price. The instalments do add to the ticket price, which is exactly why the fees are the whole answer.

BNPL: instalments always add to the purchase price, so the extra cost is fees only. Total cost = purchase price + account fees + late fees. Headphones: 480 + 6 x 2 = 492 on time (2.5% extra), or 502 with one 10 late fee (4.6% extra) (dollars).

Pause, copy the BNPL total-cost rule into your book, and write beside it the two headphone totals, 492 paid on time and 502 with one missed payment, so you can see what a single late fee does.

True or False: because a buy now pay later plan charges 0% interest, it always costs the same as paying cash.
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Putting The Methods Side By Side

Once you can total each method, comparing them is bookkeeping.

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Putting The Methods Side By Side

Once you can total each method, comparing them is bookkeeping. Work out the total cost of every option, line them up, and state the difference in dollars. The trick is to be strict about totalling every method the same way, so nothing is left out of one column and counted in another.

A laptop has a cash price of $\$1{,}600$. Three ways to buy it:

  • Cash: $\$1{,}600$.
  • Terms: 20% deposit and 18 monthly repayments of $\$78$. Deposit $= 1600 \times 0.20 = \$320$, repayments $= 18 \times 78 = \$1{,}404$, total $= 320 + 1404 = \$1{,}724$.
  • BNPL: 8 fortnightly instalments of $\$200$ with an $\$8$ monthly account fee. Instalments $= 8 \times 200 = \$1{,}600$, and 8 fortnights is 4 months, so fees $= 8 \times 4 = \$32$, total $= 1600 + 32 = \$1{,}632$.

Ranked by total cost: cash $\$1{,}600$, then BNPL $\$1{,}632$, then terms $\$1{,}724$. Against the cash price, BNPL adds $\$32$ (which is 2%) and terms adds $\$124$ (which is 7.75%).

Notice what the ranking does and does not tell you. It says terms costs $\$92$ more than BNPL for this laptop. It does not say terms is a bad choice, because it has not asked who is buying.

Must do: Compare totals against the same cash price. A percentage extra is only comparable between methods when every one of them divides by the cash price.
Common error: Comparing the size of the repayments instead of the totals. The $\$78$ monthly on terms looks smaller than the $\$200$ fortnightly on BNPL, but terms runs far longer and ends up $\$92$ dearer.

To compare purchase methods, total every method the same way and rank them, then state the gap in dollars. Laptop: cash 1600, BNPL 1600 + 32 = 1632, terms 320 + 18 x 78 = 1724. Smaller repayments do not mean a smaller total (dollars).

Pause, copy the three laptop totals into your book as a short table (cash 1600, BNPL 1632, terms 1724) with the extra beside each (0, 32, 124), so the ranking is visible at a glance.

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Justifying The Choice, Not Just Ranking It

The syllabus asks you to compare total costs and justify which method is best suited to a given context.

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Justifying The Choice, Not Just Ranking It

The syllabus asks you to compare total costs and justify which method is best suited to a given context. Those are two different jobs. The comparison is arithmetic and has one right answer. The justification depends on the person, and a good answer names the arithmetic and then names the circumstance.

Three things decide it, and a full-mark answer usually touches at least two:

  • Can they pay cash now? If yes, cash is always the cheapest, because every other method adds fees or repayment costs on top of the same ticket price.
  • Can they meet every repayment? A plan is only as cheap as its on-time total. One missed BNPL payment took the headphones from 2.5% extra to 4.6% extra.
  • How urgently is the item needed? A broken fridge cannot wait three months while you save. Paying $\$228$ extra to have it today can be the right call, and saying so is the justification.

So for the laptop: if the buyer has $\$1{,}600$ available, cash is best suited, because it is $\$32$ cheaper than BNPL and $\$124$ cheaper than terms for exactly the same laptop. If the buyer has only $\$200$ a fortnight and needs the laptop for study now, BNPL is best suited, because it costs $\$92$ less than terms and the instalments fit the fortnightly income, provided every payment is made on time.

Must do: Quote your own numbers in the justification. "BNPL is cheaper" earns little; "BNPL totals $\$1{,}632$ against $\$1{,}724$ on terms, a saving of $\$92$" earns the mark.
Common error: Answering "the cheapest one" without checking whether the buyer can actually use it. If they do not have the cash today, the cash column is not an option no matter how cheap it is.

Justifying a purchase method: name the total costs, then name the circumstance. Ask can they pay cash now, can they meet every repayment, and how urgent is the need. Cheapest is best suited only when the buyer can actually afford to use it.

Pause, copy the three justification questions into your book (cash available now, repayments affordable, urgency), and write one sentence under each about the laptop.

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Worked examples · reveal each step

Worked examples · reveal each step

Worked examples · reveal each step

WE1 · Total cost on terms. A television has a cash price of $\$2{,}400$. On terms it is a 10% deposit and 36 monthly repayments of $\$68$. Find the total cost and the extra paid as a percentage of the cash price.
Deposit $= 2400 \times 0.10 = \$240$.
Repayments $= 36 \times 68 = \$2{,}448$.
Total cost $= 240 + 2448 = \mathbf{\$2{,}688}$.
Extra paid $= 2688 - 2400 = \$288$, so $\dfrac{288}{2400} \times 100 = \mathbf{12\%}$.
Sense check: the deposit alone is $\$240$, so the 36 repayments must cover a bit more than the remaining $\$2{,}160$ for the deal to cost anything extra, and $\$2{,}448$ is $\$288$ more than that ✓.
WE2 · BNPL, on time and late. A $\$360$ jacket is bought through BNPL as 6 fortnightly instalments of $\$60$, with a $\$5$ monthly account fee. The provider charges a $\$12$ late fee per missed payment. Find the total cost if every payment is on time, and if one payment is missed.
Instalments $= 6 \times 60 = \$360$, which is exactly the purchase price, so all the extra cost is fees.
Six fortnights is 3 months, so account fees $= 5 \times 3 = \$15$.
On time: total $= 360 + 15 = \mathbf{\$375}$, which is $\dfrac{15}{360} \times 100 = \mathbf{4.2\%}$ extra (1 d.p.).
With one missed payment: total $= 375 + 12 = \mathbf{\$387}$, which is $\dfrac{27}{360} \times 100 = \mathbf{7.5\%}$ extra.
The single late fee added $\$12$, nearly as much as the three months of account fees put together.
WE3 · Comparing two plans. A washing machine has a cash price of $\$800$. On terms it is a 20% deposit and 12 monthly repayments of $\$60$. On BNPL it is 8 fortnightly instalments of $\$100$ with a $\$6$ monthly account fee. Compare the total costs.
Terms deposit $= 800 \times 0.20 = \$160$, repayments $= 12 \times 60 = \$720$, total $= 160 + 720 = \mathbf{\$880}$, so the extra is $\dfrac{80}{800} \times 100 = 10\%$.
BNPL instalments $= 8 \times 100 = \$800$, and 8 fortnights is 4 months, so fees $= 6 \times 4 = \$24$, total $= 800 + 24 = \mathbf{\$824}$, an extra of $\dfrac{24}{800} \times 100 = 3\%$.
Ranking: cash $\$800$, BNPL $\$824$, terms $\$880$.
BNPL is $880 - 824 = \mathbf{\$56}$ cheaper than terms for the same machine.
Check the percentages against each other: 3% against 10% agrees with $\$24$ against $\$80$, since both divide by the same $\$800$ ✓.
WE4 · Working backwards from a total. A sofa has a cash price of $\$1{,}500$. A store advertises it on terms as a $\$300$ deposit and 24 equal monthly repayments, with a total cost of $\$1{,}860$. Find each repayment and the extra paid as a percentage of the cash price.
The repayments must cover everything except the deposit: $1860 - 300 = \$1{,}560$.
Each repayment $= 1560 \div 24 = \mathbf{\$65}$.
Extra paid $= 1860 - 1500 = \$360$.
As a percentage of the cash price: $\dfrac{360}{1500} \times 100 = \mathbf{24\%}$.
Check forwards: $300 + 24 \times 65 = 300 + 1560 = \$1{,}860$ ✓.
A washing machine costs $\$800$ cash, $\$824$ on BNPL, or $\$880$ on terms. Priya has $\$820$ saved and needs the machine today. Which method is best suited, and why?
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