Credit Cards - How They Work
Learn how credit cards work for NSW Year 12 Mathematics Standard 1 (NESA outcome MST-12-S1-03). A credit card lets you borrow money up to a limit, and it behaves like a reducing balance loan: interest is charged on the balance still owing, purchases add to the debt and payments take it off.
You will see why a credit card counts as a reducing balance loan, find the monthly interest and the closing balance, see why the debt only falls when you pay more than the interest, and check how card interest rates stack up against those on other loans — important before you get your first card.
Theory
A credit card is a reducing-balance loan: interest is charged on the balance still owing, purchases add to the debt and payments take it off. This Year 12 Mathematics Standard 1 (NSW) guide shows how to find the monthly interest, work out the closing balance, and see why a balance only falls when you pay more than the interest.
A credit card lets you borrow money up to a limit. It works as a reducing-balance loan: each month interest is charged on the balance still owing, then purchases and payments change the balance.
The interest for the month is the monthly rate times the balance owing, e.g. \(1.5\%\) of \(\$2000=0.015\times2000=\$30\). The closing balance is opening \(+\) interest \(+\) purchases \(-\) payments. A payment lowers the balance, so less interest is charged next month; the debt only falls by payment \(-\) interest.
With no payments, interest is added to the balance and next month's interest is charged on that larger amount, so the debt keeps growing. Credit cards (about \(20\%\) p.a.) usually charge much more than a personal loan (about \(12\%\)) or a home loan (about \(6\%\)).
Interest for one month is the monthly rate (as a decimal) times the balance owing:
The closing balance for the month:
If nothing is paid, the balance grows by the rate every month (e.g. \(2\%\) per month means multiply by \(1.02\)):
How to work out a credit card balance
- Find the interest: monthly rate as a decimal \(\times\) the balance owing.
- Add the interest and any purchases to the opening balance.
- Subtract the payments to get the closing balance, then compare it with the opening balance to see whether the debt rose or fell.
Interest \(=\) rate \(\times\) balance; with no payment it is simply added on.
| \(\text{(i) interest}\) | \(=\) | \(0.015\times2600\) |
| \(\) | \(=\) | \(\$39\) |
| \(\text{(ii) balance}\) | \(=\) | \(2600+39\) |
| \(\) | \(=\) | \(\$2639\) |
Interest \(\$39\); new balance \(\$2639\).
Add the interest and purchases, subtract the payment.
| \(\text{interest}\) | \(=\) | \(0.02\times1400=\$28\) |
| \(\text{closing}\) | \(=\) | \(1400+28+260-500\) |
| \(\) | \(=\) | \(\$1188\) |
Closing balance \(\$1188\); the debt fell, because \(\$1188\lt\$1400\).
Find each month's interest, then subtract.
| \(\text{card}\) | \(=\) | \(0.0175\times3000=\$52.50\) |
| \(\text{loan}\) | \(=\) | \(0.008\times3000=\$24\) |
| \(\text{difference}\) | \(=\) | \(52.50-24\) |
| \(\) | \(=\) | \(\$28.50\) |
The credit card costs \(\$28.50\) more for the month.
Each month the balance grows by \(2\%\), so multiply by \(1.02\) twice.
| \(\text{month 1}\) | \(=\) | \(1500\times1.02=\$1530\) |
| \(\text{month 2}\) | \(=\) | \(1530\times1.02=\$1560.60\) |
Paying only the interest (\(\$30\)) each month takes off exactly what was added, so the balance stays at \(\$1500\).
\(\$1560.60\) owed; paying only the interest leaves \(\$1500\) — the debt is never repaid.
Common pitfalls
Frequently asked questions
How does a credit card work?
A credit card lets you borrow up to a limit. It works like a reducing-balance loan: each month interest is charged on the balance you still owe, purchases are added and payments are taken off.
How do you calculate interest on a credit card for one month?
Multiply the monthly interest rate, written as a decimal, by the balance owing. For example, 1.5 percent of 2600 dollars is 0.015 times 2600, which is 39 dollars.
How do you work out the closing balance on a credit card?
Closing balance equals opening balance plus interest plus purchases minus payments. For example, 1400 plus 28 plus 260 minus 500 gives a closing balance of 1188 dollars.
What happens if you only pay the interest on a credit card?
The payment only cancels out the interest that was added, so the balance stays the same and the debt is never repaid.
Why are credit cards more expensive than personal loans?
Credit cards usually charge a much higher interest rate, often around 20 percent per year, compared with about 12 percent for a personal loan and about 6 percent for a home loan. The same amount owed costs more interest on a card.