What is the difference between APR and effective annual rate?
Key takeaways
- APR is the advertised yearly rate before compounding inside the year; the effective annual rate (EAR) is what you actually pay or earn after compounding.
- A credit card quoted at 12.99% APR compounded monthly carries an effective annual rate of 13.80%.
- To compare two products with different compounding schedules, convert both to EAR and compare EAR to EAR.
Image Credits: Wikimedia Commons
APR stands for annual percentage rate. It is the yearly interest figure a lender or bank puts on the price tag, before the effect of compounding inside the year is added in.
The effective annual rate, often shortened to EAR, answers a different question: what did the money actually cost, or earn, over a full year, once interest started earning interest of its own? For most loans and savings accounts, the two numbers sit close together. They are never identical when interest compounds more than once a year.
This article explains the difference between APR and effective annual rate, including what each rate measures, how to convert one into the other, and when the gap between them matters most.
What is APR?
APR is the rate lenders advertise. On a loan, it is the simple yearly cost of borrowing before compounding is taken into account.
In the United States, APR is also a regulatory disclosure figure. It exists so borrowers can compare loan offers on a standard basis, and it folds certain fees into the calculation alongside interest, while still using simple rather than compound arithmetic, according to the finance education site OnlyCalculators.
Because it ignores compounding, APR can understate what credit really costs. Most U. S.
credit cards, for instance, are quoted as a nominal APR compounded monthly, which is not the same as the rate a cardholder actually pays on a stable balance over a year, as the Wikipedia article on annual percentage rates explains.
That is the first thing to grasp. The word "annual" in APR does not mean "what you pay over a year. " It means "the yearly figure we quote.
" The actual yearly cost is a different number.
What is the effective annual rate?
The effective annual rate is the true yearly rate once compounding is included. It tells you how much a balance actually grows, or how much a loan actually costs, over one year.
If your card compounds monthly, you pay interest on January's interest in February, on February's in March, and so on. The effective annual rate captures that whole snowball in a single yearly number.
On savings and deposit accounts, the consumer-facing version of this same calculation is called APY, or annual percentage yield. APY and EAR are the same idea under different labels, according to OnlyCalculators. So when a bank advertises 5.00% APY, it is really quoting you an effective annual rate.
The conversion between the two is where the practical value lies. Once you can move from one to the other, no advertisement can mislead you.
How to convert APR into EAR
The conversion needs one formula. EAR equals (1 plus APR divided by n), raised to the power of n, minus 1. Here n is the number of compounding periods in a year.
Take 12% APR compounded monthly. Divide 12% by 12 to get 1% per month. Raise 1.01 to the 12th power and subtract 1, and you land at about 12.68%.
A real credit card example shows the gap. A card quoted at 12.99% APR compounded monthly carries an effective annual rate of 13.7975%, roughly 13.80%, according to the worked examples on Wikipedia.
Higher rates stretch the gap further. A card at 29.99% APR compounded monthly has an effective annual rate of 34.48%, almost four and a half percentage points above the advertised figure.
Image Credits: Wikimedia Commons
How compounding frequency changes the effective rate
The more often interest compounds, the wider the gap grows. At a 12% nominal rate, monthly compounding produces an effective rate of 12.68%, while daily compounding pushes it to 12.7475%, according to OnlyCalculators.
There is also a mathematical ceiling. With continuous compounding, the formula simplifies to EAR equals e raised to the power of r, minus 1, where e is Euler's number (about 2.71828). At 12%, that ceiling is 12.7497%, only two thousandths of a point above daily compounding.
The practical upshot: the jump from annual to monthly compounding matters far more than the jump from monthly to daily. Most of the compounding effect is already captured once interest compounds monthly.
It helps to see the schedule laid out:
- Annual compounding (n = 1): the EAR equals the APR exactly.
- Quarterly compounding (n = 4): the gap is small but real.
- Monthly compounding (n = 12): the standard case for credit cards.
- Daily compounding (n = 365): slightly higher still, with diminishing returns.
So when two offers quote the same APR but compound on different schedules, the one compounding more often is the more expensive loan or the better savings account. The formula tells you exactly by how much.
When the gap between APR and EAR matters most
On small balances and short timelines, the gap is pocket change. On large balances over many years, compounding turns small gaps into serious money.
Wikipedia works through a 30-year, $200,000 loan quoted at 10.00% APR. The monthly payment comes to $1,755.87. Run the same loan with an effective annual rate of 10.00% instead, and the payment drops to $1,691.78.
The difference is $64.09 a month. Over the full 30 years, that adds up to $23,070.86, more than 11% of the original loan amount.
The lesson cuts both ways for savers. An account advertising 5.00% APY grows faster than a loan charging 5.00% APR costs you, because the APY figure already reflects compounding while the APR does not, as OnlyCalculators notes.
This is also why the golden rule of comparison is to match like with like. Comparing an APR on one offer with an APY or EAR on another is a category error. Convert both to the same measure before deciding.
Image Credits: Wikimedia Commons
FAQ
Is APR the same as the interest rate?
Not exactly. APR is a standardized yearly figure that can include certain lender fees, while the interest rate is the raw cost of borrowing. On top of that, neither one shows the effect of compounding; that is the effective annual rate's job.
Which is higher, APR or the effective annual rate?
Whenever interest compounds more than once a year, the effective annual rate is higher than the APR. If interest compounds exactly once a year, the two are identical.
Should I compare APR to APR or EAR to EAR?
Always compare like with like. APR-to-APR comparisons work for a rough ranking of loan offers, but EAR-to-EAR is the true apples-to-apples test, especially when the compounding schedules differ.
Does a higher APR always mean a more expensive loan?
Not necessarily. Because APR folds in fees and ignores compounding, two loans with the same APR can still cost different amounts. The effective annual rate, plus a look at the fee schedule, gives the fuller picture.
The bottom line
Think of APR as the price tag and the effective annual rate as the receipt. For quick comparisons, APR is fine. For the true yearly cost of a loan or the true yearly return on savings, convert each offer to its effective annual rate and compare those numbers.
This article is educational only and is not financial advice. Speak to a qualified financial professional before choosing a loan or investment product.
Rive News is the research desk behind the Rive News publication, covering the numbers behind everyday money decisions.
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