The cost of credit cards

The “nominal” rate declared by a credit card is not the real cost of the debt: monthly capitalisation pushes it up. The difference is precisely the APR.

Example — Credit cards

“Nominal” annual rate $18\%$, monthly capitalisation $m=12$: effective annual rate $(1+0{,}18/12)^{12}-1 = 1{,}015^{12}-1 \approx 0{,}1956 = 19{,}56\%.$ The APR (annual percentage rate) that banks are obliged to declare is precisely that $19{,}56\%$ — the difference from the nominal $18\%$ is the cost of the small print.

The periodic rate $0{,}18/12 = 1{,}5\%$ per month, capitalised $12$ times, produces an effective annual rate of $19{,}56\%$, higher than the nominal $18\%$. The APR makes offers with different periodicities comparable.

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Topics: Percentages
Concepts: Compound capitalisation · APR · Periodic rate
Skills: Calculating · Estimating