What it means
Lenders and banks usually quote a nominal annual rate together with a compounding frequency, such as 12% compounded monthly. Because interest charged part way through the year then earns interest itself, the amount you really pay across twelve months is higher than the headline figure suggests.
It matters most when two products quote different compounding frequencies. A card at 18% compounded daily and a loan at 18.5% compounded annually cannot be compared by eye, and converting both to an effective annual rate settles the question in one step.
The calculation takes the nominal rate, divides it by the number of compounding periods in a year, adds one, raises the result to the power of that number of periods, and subtracts one. The more often interest compounds, the further the effective rate sits above the quoted rate.
In everyday use it appears under several names. Savings products in some markets advertise an annual equivalent rate, while consumer credit rules often require an annual percentage rate that also folds in arrangement fees, so the two figures answer slightly different questions.
There is a natural ceiling to the effect. Compounding more and more frequently approaches a limit called continuous compounding, so at 12% nominal the effective rate cannot exceed about 12.75% no matter how finely the interest is sliced.
The same conversion works in both directions. Savers should compare effective rates on deposits for exactly the reason borrowers compare them on loans, and a supplier offering a settlement discount for early payment is quoting an implied rate that only becomes clear once it is annualised.
In practice
Real-world examples.
Example
A founder compares two overdraft facilities, one at 9% compounded monthly and one at 9.3% compounded annually. Converting the first gives an effective rate of roughly 9.38%, so the apparently dearer facility is in fact the cheaper of the two.
Example
A treasurer choosing between money market deposits sees 4.8% compounded daily at one bank and 4.9% compounded semi-annually at another. The effective rates come out at about 4.92% and 4.96%, and on a $10,000,000 balance that small gap is worth roughly $4,000 a year.
Example
A retailer offers customers a payment plan advertised as 1.5% a month. Expressed as an effective annual rate that is close to 19.6%, which the marketing team must disclose properly in the credit documentation. The finance director also uses the same figure internally when deciding whether the plan earns enough to justify the credit risk it carries.
Think of it
“Effective annual rate is the true yearly rate after compounding-what you really pay or earn.
Formula
Calculation
Effective annual rate = (1 + nominal rate / number of periods) raised to the power of the number of periods, minus 1. Take a business loan quoted at 12% nominal, compounded quarterly, so the rate per quarter is 0.12 / 4 = 0.03. The calculation is 1.03 x 1.03 x 1.03 x 1.03 = 1.12550881, and subtracting 1 gives 0.12550881. The effective annual rate is therefore 12.55%, so borrowing $200,000 for a year costs about $25,100 rather than the $24,000 the headline rate implies.Case study
Seen in the real world.
Marlow Interiors is a fictional furniture retailer created to illustrate this point. Needing $500,000 of working capital, the owner collected three offers and initially chose the one with the lowest quoted rate, an invoice finance line advertised at 11%.
Her accountant converted all three to effective annual rates. The 11% facility compounded weekly and worked out at roughly 11.61%.
A bank term loan quoted at 11.4% compounded annually stayed at 11.4%, and a third offer at 11.2% compounded monthly came to about 11.79%. The apparent bargain was the second most expensive of the three.
Marlow Interiors took the bank loan and saved a little over $1,000 in the first year on the same borrowing. The larger gain was procedural: the owner now asks every lender for a compounding frequency before comparing any quote, which takes a minute and removes the guesswork.
Watch out
Common mistakes.
- Comparing two quoted rates directly without checking how often each one compounds, which is the single most common error with borrowing costs.
- Assuming the effective annual rate includes fees, when arrangement and administration charges belong to the annual percentage rate calculation instead.
- Dividing an annual rate by twelve and calling the result a true monthly cost, which understates what compounding actually adds.
Questions
People also ask.
Does compounding frequency matter much at low rates?
Less than at high rates, since the gap between nominal and effective grows roughly with the square of the rate, but on large balances it is still real money.
What is continuous compounding?
It is the theoretical limit reached when interest compounds over infinitely small intervals, giving the highest effective rate any nominal rate can produce.
Which rate should a saver look at?
The effective annual rate or its local equivalent, because it is the only figure that makes accounts with different interest schedules comparable.
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