Put $10,000 somewhere at 6 per cent for a year. Compounded once a year you earn $600.00. Compounded monthly you earn $616.78. Compounded daily you earn $618.31.
The advertised rate is 6 per cent in all three cases. What differs is how often the interest is added to the balance and starts earning interest itself.
Nominal and effective
The nominal rate is the headline figure. The effective annual rate is what you actually end up paying or receiving once compounding is accounted for. At 6 per cent nominal, the effective rate is 6.00 per cent compounded annually, 6.17 per cent monthly and 6.18 per cent daily.
The gaps look small on a single year because the differences compound on interest rather than on principal. They are the reason the effective rate exists as a separate published number: it is the only figure that can be compared across products with different schedules.
The gap widens with the rate
At 6 per cent, monthly compounding adds 0.17 of a percentage point. At 20 per cent, which is ordinary credit card territory, monthly compounding turns a nominal 20 per cent into an effective 21.9 per cent. On $10,000 held for a year that is $2,193.91 rather than $2,000.00.
The higher the rate, the more there is to compound, so the further the effective rate pulls away from the nominal one. This is why compounding frequency is worth checking on debt and largely ignorable on a low-rate savings account.
Where continuous compounding fits
Push the frequency higher and the effective rate keeps rising, but by less each time. Daily compounding at 6 per cent gives 6.18 per cent, and compounding continuously, which is the mathematical limit of the process, also gives 6.18 per cent. There is nowhere further to go.
That limit is why continuous compounding appears in finance theory but rarely on a product sheet: past daily, the extra frequency buys almost nothing.
What to compare
When two products quote rates, check whether both figures are nominal or effective before comparing them. A nominal rate with monthly compounding and an effective rate that looks slightly higher can easily be the same product described two ways.
The APR and APY calculator converts between them for any schedule, and the compound interest calculator shows what the difference amounts to over a longer period, where it stops being a rounding difference.