Why can the same loan have two different interest rates?
A loan that charges 1% a month is not a 12% loan: the rate you are quoted and the rate you pay can differ, and fees can change it again.
▶ Start the storyWhen a lender says a loan costs a certain rate, the number can mean different things. The annual percentage rate, or APR, tries to express the cost of borrowing as a rate for a whole year, rather than just a monthly rate. Its job is comparison: many countries require lenders to disclose the cost of borrowing in a standard way, as a form of , so that you can set one offer next to another.
Here is why two rates can describe the same loan. Simple interest is calculated only on the amount you borrowed, ignoring . Compound interest is different: interest is added to what you owe and then earns interest itself. A rate is just the periodic rate times the number of periods in a year: 1 percent a month is a nominal 12 percent a year. Once compounding is counted, though, 1 percent a month is 12.7 percent a year, the . The same loan is described by a lower or a higher number depending on which one you quote.
Nominal rate
- Periodic rate times periods per year
- 1% a month is 12% a year
- Ignores interest on interest
Effective rate
- Counts
- 1% a month is about 12.7% a year
- Some versions also include fees
Fees add a second twist. Take a $100 loan repaid after one month, plus 5 percent and a $10 fee. Leave the fee out and the effective APR works out to about 80 percent. Include the fee and it is about 435 percent. Same loan, two very different headline numbers, and laws vary on which counts. In the United States, the Truth in Lending Act governs how APR is calculated and disclosed. In the European Union, a single calculation method has been required since 1998.
Inflation brings in a different meaning of . A nominal rate is the one before adjusting for inflation: a lender earning 8 percent when prices also rise 8 percent has a of zero.
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Recap
A nominal rate multiplies a period's rate by the periods in a year; the effective rate adds compounding, and some versions add fees too.
💡 A trick to remember it · Nominal is the name on the sticker; effective is what actually leaves the wallet after compounding and fees.
Surprising fact · A short loan can have an effective APR of about 80% or 435% for the same $100, depending on whether a $10 fee counts.
Sources (3)
No source, no claim. Every fact in this lesson (14 claims) cites at least one of these.