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Module 7 · L9 of 12 ~25 min MS12-5 ⚡ +50 XP available

Credit Cards

You buy a $2000 television on your credit card. The minimum payment is $60/month. The interest rate is 19.99% p.a. How long will it take to pay off? How much will you pay in total? The answer shocks most people: over 9 years and more than $6600 total — more than triple the original price. Credit cards are one of the most expensive forms of borrowing, yet their marketing makes them seem convenient and harmless. This lesson reveals the mathematics behind minimum payments, interest-free periods, and balance transfers.

Today's hook — You have $3000 on a credit card at 20% p.a., paying only $60/month minimum. How long until it's paid off? Predict before reading on.

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Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery — or build your own from any module’s questions.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Build custom Build your own from any module question

Recall — your gut answer first

+5 XP warm-up

You have $3000 on a credit card at 20% p.a. compounded monthly. You pay only the minimum ($60/month). Roughly how long until it's paid off?

Before reading on — write your gut prediction and reasoning. We will revisit this at the end of the lesson.

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Key ideas for this lesson

reference

Credit cards charge daily interest on the outstanding balance. Two formulas underpin almost every credit card question.

Daily interest: $I = \text{Balance} \times \dfrac{r}{365} \times \text{days}$, where $r$ is the annual rate as a decimal.

Effective annual rate: $\left(1 + \dfrac{r}{365}\right)^{365} - 1$. Daily compounding makes the effective rate higher than the advertised nominal rate.

The advertised rate is the nominal rate. Daily compounding makes the effective rate higher — a 19.99% card really costs 22.13% per year.

Daily compounding

Interest accrues every single day on whatever balance remains — even if no new purchases are made.

Minimum payment trap

When minimum payments barely cover interest, almost nothing reduces the principal — debts persist for years or even decades.

Interest-free period

Up to 55 days interest-free if the full balance is paid by the statement due date. Pay in full — pay zero interest.

What you will master

Know

Key facts

How credit card interest is calculated daily
What an interest-free period is
How effective annual rate differs from nominal rate

Understand

Concepts

Why minimum payments are a debt trap
The true cost of credit card debt
When a balance transfer saves money

Can do

Skills

Calculate daily and monthly credit card interest
Compare repayment strategies using iteration
Analyse balance transfer offers mathematically

Key terms

Nominal rateThe advertised annual interest rate before compounding effects are applied (e.g. 19.99% p.a.).

Effective annual rate (EAR)The true annual cost of borrowing after daily compounding: $(1 + r/365)^{365} - 1$.

Minimum paymentThe smallest allowed monthly repayment — typically 2–3% of the balance or a fixed floor ($25–$60).

Interest-free periodUp to 55 days with no interest charged, provided the full statement balance is paid by the due date.

Balance transferMoving debt from one card to another, usually to take advantage of a low or 0% promotional interest rate.

Transfer feeA once-off charge (typically 1–3% of the transferred balance) applied when doing a balance transfer.

How credit card interest works

core concept

Credit cards typically charge daily interest on the outstanding balance:

$$\text{Daily interest} = \text{Balance} \times \frac{r}{365}$$

where $r$ is the annual interest rate as a decimal.

Worked example: $2000 balance at 19.99% p.a.

Daily interest $= 2000 \times \dfrac{0.1999}{365} = \$1.095$/day
Monthly interest $\approx 1.095 \times 30 = \$32.85$/month
Or directly: $2000 \times \dfrac{0.1999}{12} = \$33.32$/month

Effective annual rate: $\left(1 + \dfrac{0.1999}{365}\right)^{365} - 1 \approx 22.13\%$. The advertised 19.99% becomes 22.13% p.a. due to daily compounding. Always compare effective rates when choosing between cards.

Interest-free period rule:

Purchases at the start of a billing cycle earn up to 55 days interest-free
Purchases just before the statement get approximately 25 days
If you pay the full balance by the due date — zero interest is charged
If you pay less than the full balance — interest is charged from the original purchase date

What to write in your book

Daily interest = Balance × r/365, where r is the annual rate as a decimal.
Effective annual rate = $(1 + r/365)^{365} - 1$ — always higher than the nominal rate.
Interest-free period (up to 55 days): only applies if the full balance is paid by the due date.

Quick check: A credit card has a nominal rate of 19.99% p.a. with daily compounding. The effective annual rate is:

The minimum payment trap

core concept

Minimum payments are typically 2–3% of the balance or a fixed floor ($25–$60), whichever is higher. This sounds manageable — but the mathematics is brutal.

Example: $3000 debt at 20% p.a. (compounded monthly), minimum payment $60/month.

Month	Balance	Interest	Payment	Principal reduced
1	$3000.00	$50.00	$60	$10.00
2	$2990.00	$49.83	$60	$10.17
3	$2979.83	$49.66	$60	$10.34

Using the loan repayment formula $PV = PMT \times \dfrac{1-(1+r)^{-n}}{r}$, solving gives $n \approx 111$ months = 9.25 years. Total paid $= 60 \times 111 = \$6660$. Interest paid $= \$3660$ — more than the original debt!

Comparison — paying $150/month instead: Paid off in approximately 24 months. Total paid $\approx \$3600$. Saves nearly $3000 and 7 years. The extra $90/month transforms the outcome entirely.

Why do companies set minimum payments so low? Low minimums maximise interest income for the lender. The longer the debt persists, the more the lender earns.

What to write in your book

Minimum payment (2–3% of balance) means most of each payment goes to interest, not principal.
$3000 at 20% p.a. with $60/month minimum: 111 months (9.25 years), $6660 total, $3660 interest.
Paying more than the minimum dramatically reduces term and total interest cost.

True or false: If the minimum monthly payment equals the monthly interest charge, the balance will be paid off within a few years.

Worked examples · reveal each step

PROBLEM 1 · MINIMUM PAYMENT CALCULATION

$5000 credit card debt at 19.99% p.a. compounded monthly. Minimum payment = $125 or 2.5% of balance, whichever is higher. Find the first month's interest and principal reduction. Then compare paying $300/month instead.

Month 1 interest $= 5000 \times \dfrac{0.1999}{12} = \$83.29$

Apply the monthly interest formula: Balance × r/12

PROBLEM 2 · BALANCE TRANSFER ANALYSIS

$5000 debt at 20% p.a. Balance transfer offer: 0% for 12 months with a 2% fee. Is it worthwhile if you can pay $400/month?

Transfer fee $= 5000 \times 0.02 = \$100$. New balance $= \$5100$

The 2% fee is added to the balance being transferred

Balance transfers — tool or trap?

core concept

A balance transfer moves debt to a new card with a low or 0% promotional rate.

Benefits: Pause interest accumulation; pay down principal faster.

Risks to watch:

Transfer fees (typically 1–3%)
High "revert rate" after the promotional period ends (often 20%+)
Temptation to spend on the new card, growing total debt
Missing a single payment can cancel the promotional rate immediately

Example calculation: Transfer $5000 with 2% fee ($100) to 0% for 12 months. Interest saved at 20% over 12 months $\approx \$550$. Minus $100 fee $= \$450$ net saving. But only if paid off within 12 months!

What to write in your book

Balance transfer: move debt to 0% promotional rate; save interest if cleared before promo ends.
Always calculate: net saving = interest saved − transfer fee.
Risks: revert rate, spending on new card, missing payments.

Fill the gap: A $4000 balance is transferred with a 2% fee. The transfer fee is $ and the new balance is $.

Common errors · the 3 traps that cost marks

Trap 01

Using monthly rate when daily is required

Some questions specify a number of days, not months. For 45 days: $I = \text{Balance} \times \dfrac{r}{365} \times 45$. Do not use $r/12$ for a partial month calculation.

Trap 02

Forgetting the transfer fee in balance transfer questions

The new balance after a transfer is the original debt plus the transfer fee. Always add the fee before calculating repayment schedules.

Trap 03

Assuming minimum payment always reduces the balance

If monthly interest exceeds the minimum payment, the balance actually grows — the card is never paid off. Example: $2000 at 22%, monthly interest $= \$36.67$. If minimum $= \$25$, balance increases by $\$11.67$/month.

What to write in your book

For days-based interest: use $r/365 \times$ days, not $r/12$.
Balance transfer new balance = debt + fee.
If min. payment < monthly interest, the balance grows — debt is never cleared.

Match each term to its correct description:

Quick-fire practice · 2 activities

Calculate: (a) Daily interest on $2500 at 19.99% p.a. (b) Monthly interest on the same balance. (c) Effective annual rate for 21.99% compounded daily.

A balance transfer offers 0% for 12 months with a 2% fee. You have $8000 debt at 19.99%. Is it worthwhile if you can pay $700/month? Show calculations to justify your answer.

Top 3 list: Name THREE strategies a person could use to reduce their credit card debt faster. For each, explain the mathematical reason why it works.

Revisit your thinking

Most people guess 2–3 years. The reality is much worse. At $60/month on $3000 at 20%, month 1 interest $= \$50$, so only $10 reduces the principal. Using the loan formula:

$$3000 = 60 \times \frac{1-(1+0.20/12)^{-n}}{0.20/12}$$

Solving gives $n \approx 111$ months $= 9.25$ years. Total paid $= \$6660$. Total interest $= \$3660$ — more than the original debt. This is the minimum payment trap.

What has changed in your understanding? What did you get right? What surprised you?

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Multiple choice

+5 XP per correct · +25 XP all-correct

Pick your answer, then rate your confidence — that tells the system what to drill next.

Q1. A credit card has a balance of $3000 at 20% p.a. compounded monthly. The monthly interest charge is closest to:

Q2. A minimum payment of $60/month is made on a $3000 debt at 20% p.a. The amount of principal reduced in month 1 is:

Q3. An interest-free period on a credit card applies only if:

Q4. A $6000 balance is transferred to a 0% card with a 2% fee. The new balance after the transfer is:

Q5. A card advertises 21.99% p.a. with daily compounding. The effective annual rate is:

Short answer

ApplyBand 42 marks

SA 1. A credit card has a $4500 balance at 19.99% p.a. (a) Calculate the daily and monthly interest. (b) If the minimum payment is $112.50 (2.5%), how much principal is paid off in month 1? (c) Approximately how many months to clear the debt paying only the minimum? (2 marks)

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ApplyBand 42 marks

SA 2. A balance transfer offers 0% for 15 months with a 1.5% fee on a $6000 debt currently at 20% p.a. (a) Calculate the transfer fee. (b) If you pay $400/month, will the debt be cleared before the promotional period ends? (c) Calculate the total saving compared to staying on the current card at $400/month. (2 marks)

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AnalyseBand 53 marks

SA 3. (a) A credit card charges 22% p.a. compounded monthly. The minimum payment is $25. For a $2000 balance, show that the debt can never be cleared with this minimum payment. (b) The same card offers 1% cashback on purchases. A customer spends $1000/month and carries a $3000 balance. Does the cashback exceed the monthly interest cost? (c) Explain mathematically why credit card debt at 20%+ p.a. is one of the most expensive forms of borrowing. (3 marks)

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Comprehensive answers (click to reveal)

MC 1 — B: $3000 × 0.20/12 = $50.00/month.

MC 2 — C: Interest = $50. Payment = $60. Principal = $60 − $50 = $10.

MC 3 — A: Interest-free period requires the full balance to be paid by the due date every month.

MC 4 — D: Fee = $6000 × 0.02 = $120. New balance = $6000 + $120 = $6120.

MC 5 — B: EAR = (1 + 0.2199/365)³⁶⁵ − 1 ≈ 24.6%, higher than the nominal rate.

SA 1 (2 marks): (a) Daily = $2.46, Monthly = $74.96 [0.5]. (b) Principal = 112.50 − 74.96 = $37.54 [0.5]. (c) n ≈ 280 months (~23 years) [1].

SA 2 (2 marks): (a) Fee = $90. New balance = $6090 [0.5]. (b) $6090/$400 = 15.2 months — just over 15, barely not cleared [0.5]. (c) Without transfer at $400/month on 20%: n ≈ 18 months, total = $7200. With transfer: $6090 total. Saving ≈ $1110 [1].

SA 3 (3 marks): (a) Monthly interest = $2000 × 0.22/12 = $36.67. Min payment = $25 < $36.67 — balance grows by $11.67/month, debt never cleared [1]. (b) Cashback = $10/month. Interest = 3000 × 0.22/12 = $55/month. Net loss = $45/month [1]. (c) At 22% compounded daily, effective rate ≈ 24.6%, exceeding average investment returns (7–10%), wage growth (2–3%), and inflation (2–3%). Exponential growth works against the borrower; high rates and low minimums create a trap where balances persist for decades [1].

Drill 1: (a) $1.37/day. (b) $41.63/month. (c) EAR = (1+0.2199/365)³⁶⁵ − 1 ≈ 24.6%.

Drill 2: Fee = $160. New balance = $8160. Months = 8160/700 = 11.7 — cleared before 12 months. Interest on original card at $700/month over ~13 months ≈ $600. Net saving ≈ $440. Transfer is worthwhile.

Boss battle · The Credit Card Examiner

earn bronze · silver · gold

Five timed questions on credit card interest, minimum payments, effective rates, and balance transfers. Beat the boss to bank a tier — gold (90% + speed), silver (75%), or bronze (50%). Replays welcome.

⚔ Enter the arena

Science Jump · platform challenge

Climb platforms by answering questions on credit cards. Pool: lesson 9.

Mark lesson as complete

Tick when you've finished the practice and review.

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Module overview · Maths Standard