APR, AER and the numbers lenders quote

Four rates, one product

The same borrowing can be described with four different percentages, all of them honest, all of them measuring something slightly different. Knowing which one is on the page in front of you is most of the work.

• Nominal rate — the interest charged on the outstanding balance, before any fee and before any compounding is taken into account. It is sometimes quoted per month rather than per year, particularly on revolving credit.
• APR — the annual percentage rate. A standardised cost-of-credit figure that includes the interest plus any charge you must pay in order to have the credit at all, spread across the life of the agreement.
• AER — the annual equivalent rate, used on savings. It shows what a year's interest comes to once compounding is allowed for, so that accounts paying monthly and annually can be lined up beside each other.
• EAR — the effective annual rate, the same compounding calculation applied to borrowing, most often on overdrafts.

APR and AER are not two views of the same number, and they are not comparable to each other. APR answers "what does this cost me in total, per year, as a percentage of what I borrowed". AER answers "what does a year of compounding turn this rate into". A product can be described by both, and the two figures will not match.

What a nominal rate leaves out

A nominal rate is a true statement about interest and a poor description of cost. Three things routinely sit outside it.

The first is the period. A card quoted at 1.5% a month is not a 1.5% product, and it is not straightforwardly an 18% product either. Multiplying a monthly rate by twelve gives the nominal annual rate; it ignores the fact that unpaid interest joins the balance each month and is charged interest in turn.

The second is fees. An arrangement fee, a product fee, a completion fee or a fee deducted from the amount advanced all raise the cost of the borrowing without touching the interest rate. Two offers can carry identical nominal rates and cost materially different amounts.

The third is timing. When a fee is paid matters. A fee taken out of the money you receive means you are paying interest on an amount larger than the amount that reached you.

How APR folds in the fees

APR exists to close those gaps. It is a single annualised percentage that takes the interest and the compulsory charges together and asks what rate would produce that total cost over that period on that amount borrowed.

Round arithmetic makes the point. Take $1,000 borrowed for one year and repaid in a single payment at the end. On a 12% nominal rate with no fee, the interest is $120, the total repaid is $1,120, and the cost of credit is $120 on $1,000 — an APR of 12%. Now take a 10% nominal rate with a $50 arrangement fee added to the agreement. The interest is $100, the fee is $50, the cost is $150 on $1,000, and the APR is 15%. The offer with the lower headline rate is the more expensive one.

Timing shifts it again. Go back to the 12% rate, but have the $50 fee deducted before the money is advanced: you receive $950 and still repay $1,120. The cost is $170 measured against the $950 you actually got, which is roughly 17.9%.

Real agreements repay in instalments rather than in one lump, so a published APR is the output of a prescribed calculation rather than a division you can do in your head. The principle survives the complication: APR captures interest plus unavoidable fees, annualised.

What it generally does not capture is anything optional or conditional. Charges commonly excluded include late payment and missed payment fees, charges for exceeding a limit, cash withdrawal fees on a card, foreign currency loading, optional insurance or protection cover, and in some cases early repayment charges. APR also assumes the agreement runs as written — drawn down when expected, repaid on schedule, to full term. Repay early, pay late, or use the credit differently from the assumed pattern, and the rate you actually paid will differ from the rate advertised.

What AER and EAR measure

Compounding is the reason a rate and a year's worth of that rate are different things. AER states the second figure. Take a 12% nominal rate and vary only how often interest is added to the balance.

The gap widens as rates rise. A card charging 1.5% a month has a nominal annual rate of 18%, but twelve months of compounding at 1.5% comes to about 19.6% — that is the EAR, and the difference is the interest charged on interest.

On savings, AER is what allows two accounts to be compared when one pays interest monthly and one pays annually. It carries assumptions of its own: that the balance stays put for twelve months, that interest is left in the account rather than withdrawn, and that the rate holds. Where an account pays an introductory bonus for a fixed period, the quoted AER usually reflects the first twelve months, so the rate after the bonus expires is a separate question. Tax treatment sits outside AER entirely.

Why representative is not a quote

Advertised borrowing rates are usually labelled representative APR, and the label is a legal qualification rather than decoration. In several jurisdictions, advertising rules require the representative figure to be a rate that a defined majority of successful applicants actually receive, with the threshold set by the rules in force rather than by the lender. That leaves a substantial minority who are accepted at a higher rate, and it says nothing at all about applicants who are declined.

Two mechanisms push individual rates away from the headline. The first is risk-based pricing: the rate offered reflects the lender's assessment of the applicant, so credit history, income, existing commitments and the lender's own appetite all feed the number. The second is banding by size or term. Unsecured personal loan pricing is often tiered, and the best-advertised rate frequently sits in a middle band rather than at the smallest amounts — a $2,000 loan and a $12,000 loan from the same lender may be priced quite differently.

The consequence is that the only rate that describes what you would pay is a personalised quotation. Many lenders and comparison services offer an eligibility or quotation check that indicates a likely rate using a search recorded in a way that does not affect a credit file in the same manner as a full application. Whether a given check works that way is stated in its own terms, and worth reading before clicking, because a run of full applications in a short window is itself visible to later lenders.

Comparing two offers honestly

Rates can only be compared when the things around them are held still. A few inputs do most of the work.

• Same amount, same term, same schedule. A lower rate over a longer term can cost more in total than a higher rate over a shorter one, because interest is charged for longer.
• Total amount payable, in currency. Credit agreements normally state the total figure alongside the rate. Comparing two dollar totals removes most of the ambiguity that comparing two percentages introduces.
• Which fees are inside the APR and which are not. If an offer has a fee excluded from its APR because it is technically optional, the exclusion is only meaningful if you genuinely would not pay it.
• Fixed or variable. A quoted APR on a variable-rate agreement describes the cost if the rate never moves. On a long agreement that assumption carries most of the uncertainty.
• Promotional periods and the charge for entering them. A 0% balance transfer is not free if it carries a transfer fee. A 3% fee on $3,000 is $90, which is 3% of the balance spread over the promotional period — 2% a year across eighteen months, and more than that in effect, because the balance shrinks as it is repaid while the fee was charged on the full amount.
• What happens at the end. The rate a promotional balance reverts to, and whether repayments are applied to the promotional balance or the standard one, can matter more than the promotional rate itself.

What this means in practice

The four rates are answers to four different questions, and most confusion comes from reading one as though it answered another. A nominal rate describes interest. An APR describes the cost of credit including the fees you cannot avoid. AER and EAR describe what compounding does to a rate over a year. Representative APR describes an advertising threshold, not an offer.

A reader holding two offers has a few things worth checking before the percentages are treated as comparable: whether the amounts and terms match, what the total amount payable is in currency on each, which charges sit inside each quoted rate and which are excluded, whether either rate is variable, and whether the figure on the page is representative or personalised. Where an agreement is long, secured, or complicated by early repayment terms, the fine print carries more of the cost than the headline does, and a qualified professional who knows the full circumstances is better placed to read it than any general explanation can be.

The figures above are round illustrations chosen so the arithmetic can be followed, not statements about any product; real rates vary by lender, by applicant and over time. The takeaway is a habit rather than a number: identify which rate is quoted, ask what it excludes, and convert the comparison into a total in dollars before deciding one offer is cheaper.