APR, AER, APY and nominal rates: what interest rates really mean

Two products can both advertise “5%” and still charge or pay different amounts of money. The difference comes down to two questions: how often interest is added, and whether the quoted figure already includes that compounding (and any fees). Once you can answer those, APR, AER, APY, EAR and nominal rates stop being alphabet soup and become simple conversions.

Nominal rates and effective rates

A nominal annual rate is a headline number that is divided up across the year. A 6% nominal rate charged monthly means 0.5% is applied each month. Nothing in the 6% figure tells you what happens when interest is added to the balance and then itself earns or attracts interest.

An effective annual rate (often shortened to EAR) answers exactly that question. It is the single rate that, applied once at the end of the year, produces the same result as all the smaller, compounded steps within the year. The formula is:

effective rate = (1 + nominal rate ÷ n)n − 1, where n is the number of compounding periods per year.

Almost every consumer rate you meet is one or the other. Savings rates labelled AER or APY are effective rates. Loan and mortgage rates labelled “interest rate”, “nominal rate” or, in the US and Canada, APR, are usually nominal rates divided by the number of payments. In the UK and the EU, the APR on a loan is an effective annual rate that also folds in compulsory fees. Knowing which convention a figure follows is most of the battle.

How compounding frequency changes the same rate

The table below takes one nominal rate, 5%, and shows the effective annual rate it produces under different compounding schedules. Every figure was computed from the formula above.

Two things stand out. First, the effective rate is always at least as high as the nominal rate when the rate is positive. Second, the gains shrink quickly: moving from annual to monthly compounding adds about 0.116 percentage points, while moving from monthly to daily adds only about 0.01. Over long periods, though, even small gaps add up. In the compound interest calculator, 10,000 at 5% for ten years grows to 16,288.95 with annual compounding and 16,470.09 with monthly compounding, a difference of 181.14 from compounding alone.

AER and APY: effective rates for savings

Savings providers in the UK quote an AER (annual equivalent rate). It shows what the account would pay over a year if interest were added once and left in the account, so an account paying monthly and one paying annually can be compared on the same footing. The FCA’s summary box format for savings accounts allows the interest rate to be shown as an AER, with the calculation following an industry practice note.

In the US, the equivalent is the APY (annual percentage yield). Regulation DD, which implements the Truth in Savings Act, defines APY as a percentage rate reflecting the total interest paid on an account, based on the interest rate and the frequency of compounding over a 365-day period. Banks must disclose it, so APY is the figure designed for side-by-side comparison.

Some savings accounts also quote a “gross” rate alongside the AER. Where that gross figure is the nominal rate before compounding, a monthly-interest option can show a lower gross rate than an annual-interest option and still have exactly the same AER: 4.889% paid monthly and 5% paid annually both work out at 5% over a year.

APR: the cost of borrowing, defined differently by country

APR (annual percentage rate) is the headline cost figure for credit almost everywhere, but the arithmetic behind it is not universal.

United States: a nominal rate that includes fees

Under Regulation Z, which implements the Truth in Lending Act, the APR on closed-end credit is the nominal annual rate found by multiplying the rate per unit-period by the number of unit-periods in a year. A loan charging 0.5% a month therefore has an APR of 6%, even though its effective annual rate is about 6.168%. The APR must be disclosed alongside the finance charge, and it is described on disclosures as “the cost of your credit as a yearly rate”. For mortgages, the CFPB explains that APR reflects the interest rate plus points, broker fees and certain other charges, which is why it is usually higher than the note rate.

UK and EU: an effective rate that includes fees

The EU Consumer Credit Directive defines the APRC (annual percentage rate of charge) through an equation that discounts every drawdown and repayment on an annual compounding basis, so the result is an effective annual rate. UK consumer credit rules follow the same approach. The practical result is that, with no fees at all, a UK APR is higher than the monthly nominal rate that produces the same payments.

UK adverts also feature a representative APR. Under the FCA’s rules, this is a rate at or below which the firm reasonably expects at least 51% of the agreements resulting from the promotion to be made. The rate an individual is offered can be higher. In 2026 the FCA consulted on whether representative APR disclosures and the 51% threshold still help consumers understand the cost of credit, so the rules may change.

Worked example: one loan, two kinds of APR

You can reproduce both figures in the loan calculator by switching the rate type. The point is not that one convention is cheaper; it is that the same number means different things, so it pays to check which one a quote uses before comparing it with another.

Canadian mortgages: semi-annual compounding

Section 6 of Canada’s Interest Act says that no interest is recoverable on a blended-payment mortgage unless the mortgage contains a statement showing the principal and the rate of interest “calculated yearly or half-yearly, not in advance”. In practice, fixed-rate Canadian mortgages are typically compounded twice a year while being paid monthly. The FCAC’s model disclosure box for a fixed-rate mortgage, for example, describes the rate as compounded twice per year but charged monthly, and CMHC’s mortgage-backed securities standards describe the typical Canadian mortgage as having monthly payments and a rate compounded semi-annually.

To find the monthly rate, convert the semi-annual rate into six equal monthly steps:

The mortgage calculator has a Canada preset that applies this conversion automatically. Variable-rate Canadian mortgages can follow different conventions, so the contract’s own wording is what counts.

Converting between rate types

Three formulas cover almost every conversion you will need. In each, n is the number of periods per year.

• Nominal to effective: effective = (1 + nominal ÷ n)ⁿ − 1.
• Effective to rate per period: per-period = (1 + effective)^1/n − 1.
• Effective to nominal: nominal = n × ((1 + effective)^1/n − 1).

For example, a 5% AER corresponds to a monthly rate of about 0.4074% and a nominal rate, compounded monthly, of about 4.889%. Run the other way, 4.889% nominal compounded monthly returns 5% effective. If you are setting up a savings plan in the savings goal calculator with an account quoted as an AER, choose the effective rate type and the tool performs this conversion for you.

Comparing rates fairly

A few habits make comparisons reliable regardless of country:

• Compare like with like. Put both rates on an effective annual basis before deciding which is higher. A 4.95% AER looks higher than a 4.9% nominal rate compounded monthly, yet the 4.9% rate works out at about 5.012% effective, so on paper it pays more over a year.
• Check what is included. APRs usually include compulsory fees; plain interest rates usually do not. A low rate with a large arrangement fee can cost more than a higher rate with none, especially on short or small loans.
• Check whether the rate is fixed. A variable or introductory rate can change, and any APR quoted is based on assumptions about what happens next.
• Look at the money, not just the percentage. Total interest and total repaid, shown by the loan calculator and the mortgage calculator, are the figures that land in your bank account.

Interest rates are also central to two of our other guides: debt avalanche vs debt snowball shows how rate ordering changes total interest across several debts, and overpaying a mortgage or saving compares a borrowing rate with an after-tax savings rate. Every formula on this page, including our rounding rules, is documented on the methodology page.

This guide explains how things work in general terms. It isn’t financial, tax or legal advice. Spotted something out of date? Email errors@moneyotter.com and we’ll check it against the source.