APR versus APY
These two rates describe the same loan or savings account but answer different questions. The APR (annual percentage rate) is the nominal, advertised rate — the number before compounding. The APY (annual percentage yield, sometimes called the effective annual rate) is what you actually pay or earn once the interest compounds over the year. Whenever interest is added more than once a year, the APY is higher than the APR, because you earn interest on interest.
Why the frequency matters
The gap widens with both the rate and the compounding frequency:
APY = (1 + APR/n)ⁿ − 1
where n is the number of compounding periods per year. As n grows toward infinity the formula approaches continuous compounding, APY = e^APR − 1. For a 5% APR the effective yield climbs from 5.000% compounded annually to 5.116% monthly, 5.127% daily, and 5.127% continuous — the last few steps barely move, because monthly compounding already captures most of the effect.
The credit-card example
Credit cards advertise an APR but compound the balance daily. A card quoting 24% APR actually charges an effective 27.11% a year: (1 + 0.24/365)³⁶⁵ − 1 = 0.2711. That 3-point difference is real money on a carried balance, and it is why comparing a card's APR to a savings account's APY is comparing two different things. Always convert both to the same basis before comparing.
When it does and doesn't matter
At low rates and low frequencies the difference is small enough to ignore — a 2% APR compounded monthly is 2.018% APY. At high rates, high frequencies, or long horizons it compounds into something significant. This calculator shows every frequency at once so the size of the effect is visible for your specific rate.
Related tools: the break-even and margin calculator for the other side of small-business math, and the Black-Scholes calculator, whose risk-free rate is a continuously compounded APR.