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Module 7 · L9 of 12 ~25 min MST-12-S2-02 ⚡ +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.
0/5QUESTS

Get oriented

Recall what you already know, meet the key ideas and settle the terms.

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
01
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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02
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.

How daily credit-card interest is charged.
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.
03
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
04
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.

See how the interest works

Follow the daily rate, the interest-free period and what ends it.

05
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

Credit card interest is calculated daily on the outstanding balance (daily rate = annual rate ÷ 365). Most cards offer an interest-free period (typically 44–55 days) only if the full balance is paid by the due date.

Pause, copy the daily rate formula (daily rate = annual rate ÷ 365) and the interest-free period condition: no interest is charged only if the entire statement balance is paid in full by the due date into your book.

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

See the minimum payment trap

Work out how long a balance takes to clear when you pay only the minimum.

06
The minimum payment trap
core concept

Credit card interest is calculated daily at daily rate = annual rate ÷ 365, compounding on the outstanding balance. The interest-free period (typically 44–55 days) only applies if the full balance is paid by the due date. If only the minimum payment is made, usually 2–3% of the balance, almost all of that payment is swallowed by interest, the principal barely decreases, and a $3,000 debt can take over 20 years to clear.

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.

The minimum payment trap: paying only the minimum each month means most of the payment is interest, and the balance falls very slowly. A $3,000 debt at 20% p.a. paying minimum 2% can take over 20 years to repay.

Pause, copy the minimum payment trap: minimum ≈ 2% of balance means most of each payment is interest and the balance barely falls, a $3,000 debt at 20% p.a. with only minimum payments can take 20+ years to repay and cost more than the original debt in interest into your book.

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

Judge a balance transfer

Decide when a transfer offer is a tool and when it is a trap.

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.

1
Month 1 interest $= 5000 \times \dfrac{0.1999}{12} = \$83.29$
Apply the monthly interest formula: Balance × r/12
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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?

1
Transfer fee $= 5000 \times 0.02 = \$100$. New balance $= \$5100$
The 2% fee is added to the balance being transferred
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08
Balance transfers, tool or trap?
core concept

Paying only the minimum means the balance barely falls and total interest cost multiplies dramatically over years. A balance transfer moves existing debt to a low (often 0%) promotional rate, which can save a significant amount of interest. But it is only advantageous if (1) the transfer fee is less than the interest saved, and (2) the full balance is repaid before the promotional rate expires and reverts to a standard high rate.

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!

A balance transfer moves debt to a lower (often 0%) rate for a promotional period. It is advantageous only if: (1) the transfer fee is less than the interest saved, and (2) the full balance is repaid before the promotional rate expires.

Pause, copy the two conditions for a balance transfer to be advantageous: (1) transfer fee < total interest saved during the promotional period; (2) full balance is repaid before the promotional low rate expires into your book.

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

Avoid the credit card traps

Fix the daily-versus-monthly rate slips that cost marks.

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.

Match each term to its correct description:

  • Nominal rate
  • Effective annual rate
  • Balance transfer
  • Interest-free period
  • Moving debt to a card with a promotional rate
  • Up to 55 days with no interest if full balance paid
  • Advertised annual rate before compounding
  • True cost after daily compounding

Drill it and revisit

Run the drill, then return to your opening answer and name what has changed.

Quick-fire practice · 2 activities

1

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.

2

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.

09
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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Practise credit cards

Answer the question bank, then write full short-answer responses.

01
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:

02
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.