Nominal vs. effective interest rate

Two numbers for one rate

An interest rate is almost always quoted per year, but interest is often added more often than once a year — quarterly, monthly or daily. When it is, each addition starts earning interest of its own before the year is out, and the year ends a little higher than the quoted rate implies.

That gives two ways to state the same rate. The nominal rate is the yearly figure before compounding: 6% a year added monthly means 0.5% each month. The effective annual rate is what that actually adds up to over a whole year once the compounding is counted.

Different places use different labels. In the US, savings accounts advertise an APY, which includes compounding, while loans and cards advertise an APR, which generally does not. In the UK and the EU, credit offers must show an APRC, which also folds in most of the fees.

The conversion

With a nominal rate r, added n times a year:

effective annual rate = (1 + r ÷ n)ⁿ − 1

For 6% added monthly: 1.005 multiplied by itself twelve times is 1.06168, so the effective rate is 6.168%. The more often interest is added, the higher the effective rate — but each step up adds less than the one before.

How much the frequency changes

Here is the same 6% nominal rate at each of the calculator's compounding frequencies, with £5,000 left for ten years.

Going from once a year to daily adds £156 over the decade. That is real money, but compare it with one percentage point of rate: the same amount at 7% compounded annually ends £882 ahead of 6%, more than five times as much. When comparing savings accounts, the rate matters far more than how often it is applied.

On a loan, the gap is wider

The difference between nominal and effective grows with the rate. At 12% added monthly, the effective rate is 12.68%. At 20% — a common level for credit cards — it is 21.94%. A card quoted at 20% costs almost 22% a year on a balance left unpaid.

That is why the effective figure is the one to look at when borrowing. It is also why debt that is carried from month to month grows faster than most people expect, which the guide on how debt compounds works through in detail.

Comparing like with like

• Compare effective rates with effective rates, never an effective rate with a nominal one.
• When two offers both quote nominal rates, check how often each adds interest before deciding which is higher.
• For borrowing, the APRC or its local equivalent is closer to the true yearly cost, because it includes fees.

The calculator takes a nominal rate and lets you choose the compounding frequency, so you can see the effect directly. For daily compounding it converts the rate to an equivalent monthly one, since contributions are made monthly.

The figures here are arithmetic on a fixed rate. Real accounts and loans can change their rates, and nothing here is financial advice.