Effective interest rate

Banks add interest at different intervals: once a year in one place, every month in another. Two offers showing the same figure on the leaflet can therefore differ in reality. The effective rate converts them into one comparable number for the year.

Why two identical figures are not identical

If interest is added monthly, the interest credited in January starts earning on its own from February. By the end of the year it has produced further interest. With annual compounding no such chance arises.

The figure quoted in an offer is the nominal rate. The effective rate is what is actually left of it after a year, and with more frequent compounding it is always higher.

The formula

$$EAR = \left(1 + \frac{r}{n}\right)^{n} - 1$$

• $r$: the nominal annual rate as a decimal
• $n$: the number of times interest is added per year

If interest is added once a year ($n = 1$), the effective rate equals the nominal one. At every higher $n$ the gap widens, though its increments get smaller.

A worked example

Two banks offer 12% a year. The first adds interest once a year, the second every month.

• Annual compounding: the effective rate is 12.00%
• Monthly compounding: the effective rate is 12.68%

A difference of 0.68 percentage points looks unremarkable, but on €50,000 it is roughly €340 a year and with compound interest it builds over time.

The effective rate and the APRC

For loans, Slovakia requires the APRC (annual percentage rate of charge) to be stated. It rests on the same idea but goes further: alongside the payment frequency it includes fees, insurance and the loan's other compulsory costs.

A rule for comparing

For deposits, compare the effective interest rate. For loans, compare the APRC, not the interest rate on its own.

Where you will use it

The effective rate is the only fair way to compare savings accounts, term deposits or bonds with different compounding frequencies. The same principle sits behind converting an annual rate into a monthly one for an annuity instalment.

The compound interest calculator works out the effective rate automatically whenever the frequency changes.