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Disclaimer
This calculator provides estimates for informational purposes only and does not constitute financial, medical, legal, or tax advice. Always consult a qualified professional about your specific situation.
How APY Is Calculated
APY (Annual Percentage Yield) is the actual amount an account earns in a year once compounding
is factored in — always equal to or higher than the account’s stated nominal rate. Enter the
nominal annual rate and how often interest compounds, and this calculator converts it into the
real effective yield, plus shows how that yield changes across every common compounding schedule.
This is distinct from the Compound Interest Calculator calculator, which projects a
starting balance (plus optional ongoing contributions) forward over many years to show how it
grows over time. This calculator answers a narrower question first: for a single year, what does
a given nominal rate and compounding schedule actually yield?
The Formula
APY=(1+nr)n−1
where r is the nominal annual rate as a decimal and n is the number of compounding
periods per year. As n grows without bound this converges to the continuous-compounding
formula:
For comparison at the same 5% nominal rate: annually compounded gives exactly 5.000%,
quarterly gives 5.095%, daily gives 5.127%, and continuous compounding gives
5.127% — almost identical to daily.
The gap between annual and monthly compounding here is about 0.116 percentage points —
a real but modest difference at this rate.
Key Factors to Consider
APY assumes the rate stays constant for the full year. Many savings accounts and CDs have
variable or promotional rates that change over time — the APY quoted today reflects only the
current rate, not a guarantee of what the account will actually earn over the next 12 months if
the rate changes.
Fees can eat into the effective yield a bank’s advertised APY implies. A monthly maintenance
fee or a minimum-balance penalty reduces the actual amount you keep, even though it doesn’t
change the account’s advertised APY figure — always check for fees separately when comparing
accounts.
APY and APR describe different things and shouldn’t be confused. APY (yield) describes what
a deposit account like a savings account or CD EARNS you; APR describes what a loan or credit
product COSTS you to borrow — they use related math, but apply to opposite sides of a
transaction.
Compounding frequency has diminishing returns. As the worked example shows, moving from
monthly to daily to continuous compounding narrows the gap sharply — a bank rarely needs to
compound more than daily to capture nearly all the realistic benefit.
Interpreting Your Results
A bank advertising a 5% APY on a savings account is already telling you the effective yield,
compounding included — you don’t need to do any further math to compare it against another
bank’s own advertised APY. But when you’re only given a nominal rate (common on CDs, loans,
and some promotional offers) alongside a compounding schedule, this calculator’s job is to
convert that into the same apples-to-apples APY figure so the two numbers can be compared fairly.
The gap between a nominal rate and its APY grows with both the rate itself and how often it
compounds — at low rates and modest compounding (like most everyday savings accounts) that gap is
usually a fraction of a percentage point, not enough to change a decision by itself, but worth
checking whenever two offers look close.
Common Mistakes
Comparing accounts by nominal rate instead of APY. Two accounts with the same stated rate
but different compounding schedules don’t actually pay the same amount — APY is the number
that makes the comparison fair.
Assuming more frequent compounding always makes a big difference. As the worked example
shows, the gain from monthly to daily to continuous compounding shrinks quickly — most of the
real-world benefit is already captured well before continuous compounding.
Confusing APY with a multi-year growth projection. APY describes one year’s yield only —
for how a balance grows over several years, use the Compound Interest Calculator instead.
Cómo Se Calcula El APY
El APY (Rendimiento Anual Efectivo) es la cantidad real que una cuenta gana en un año una vez
que se tiene en cuenta la capitalización — siempre igual o mayor que la tasa nominal indicada de
la cuenta. Ingresa la tasa anual nominal y con qué frecuencia se capitaliza el interés, y esta
calculadora la convierte en el rendimiento efectivo real, además de mostrar cómo cambia ese
rendimiento según cada plan de capitalización común.
Esto es distinto de la calculadora Calculadora de Interés Compuesto, que proyecta un saldo
inicial (más depósitos continuos opcionales) durante muchos años para mostrar cómo crece con el
tiempo. Esta calculadora responde primero una pregunta más específica: para un solo año, ¿qué
rendimiento produce realmente una tasa nominal y un plan de capitalización dados?
La Fórmula
APY=(1+nr)n−1
donde r es la tasa anual nominal como decimal y n es el número de períodos de
capitalización por año. A medida que n crece sin límite, esto converge a la fórmula de
capitalización continua:
APYcontinua=er−1
Ejemplo Resuelto
Una tasa nominal del 5% capitalizada mensualmente:
Para comparar con la misma tasa nominal del 5%: la capitalización anual da exactamente
5.000%, la trimestral 5.095%, la diaria 5.127%, y la capitalización continua da
5.127% — casi idéntica a la diaria.
La diferencia entre capitalización anual y mensual aquí es de aproximadamente 0.116 puntos
porcentuales — una diferencia real pero modesta a esta tasa.
Factores Clave a Considerar
El APY asume que la tasa se mantiene constante durante todo el año. Muchas cuentas de
ahorro y CD tienen tasas variables o promocionales que cambian con el tiempo — el APY indicado
hoy refleja solo la tasa actual, no una garantía de lo que la cuenta realmente ganará en los
próximos 12 meses si la tasa cambia.
Las comisiones pueden reducir el rendimiento efectivo que implica el APY anunciado por un
banco. Una comisión mensual de mantenimiento o una penalización por saldo mínimo reduce la
cantidad real que conservas, aunque no cambie la cifra de APY anunciada de la cuenta — siempre
revisa las comisiones por separado al comparar cuentas.
El APY y la TAE (APR) describen cosas distintas y no deben confundirse. El APY (rendimiento)
describe lo que una cuenta de depósito, como una cuenta de ahorro o un CD, te HACE GANAR; la
TAE describe lo que un préstamo o producto de crédito te CUESTA pedir prestado — usan
matemáticas relacionadas, pero se aplican a lados opuestos de una transacción.
La frecuencia de capitalización tiene rendimientos decrecientes. Como muestra el ejemplo
resuelto, pasar de mensual a diaria y luego a continua reduce la diferencia rápidamente — un
banco rara vez necesita capitalizar con más frecuencia que a diario para capturar casi todo el
beneficio realista.
Cómo Interpretar Tus Resultados
Un banco que anuncia un APY del 5% en una cuenta de ahorro ya te está indicando el rendimiento
efectivo, capitalización incluida — no necesitas hacer ningún cálculo adicional para compararlo
con el APY anunciado por otro banco. Pero cuando solo se te indica una tasa nominal (algo común en
CD, préstamos y algunas ofertas promocionales) junto con un plan de capitalización, el trabajo de
esta calculadora es convertir eso en la misma cifra de APY comparable para que ambos números
puedan compararse de forma justa. La diferencia entre una tasa nominal y su APY crece tanto con la
tasa misma como con la frecuencia de capitalización — con tasas bajas y capitalización modesta
(como en la mayoría de las cuentas de ahorro comunes) esa diferencia suele ser una fracción de un
punto porcentual, no suficiente para cambiar una decisión por sí sola, pero vale la pena revisarla
cuando dos ofertas parecen similares.
Errores Comunes
Comparar cuentas por la tasa nominal en lugar del APY. Dos cuentas con la misma tasa
indicada pero diferentes planes de capitalización en realidad no pagan la misma cantidad — el
APY es el número que hace justa la comparación.
Suponer que una capitalización más frecuente siempre marca una gran diferencia. Como
muestra el ejemplo resuelto, la ganancia de mensual a diaria y luego a continua se reduce
rápidamente — la mayor parte del beneficio real ya se captura mucho antes de la capitalización
continua.
Confundir el APY con una proyección de crecimiento de varios años. El APY describe solo el
rendimiento de un año — para el crecimiento de un saldo a lo largo de varios años, usa en su
lugar la Calculadora de Interés Compuesto.
Why does compounding frequency change my yield if the rate stays the same?
Interest that compounds more often starts earning interest on itself sooner. Two accounts with the identical stated (nominal) rate can end up paying different actual amounts over a year depending on whether interest is credited annually, monthly, or daily -- APY is the number that already accounts for this, so it is the fair way to compare accounts.
What does "continuous compounding" actually mean?
It's the mathematical limit of compounding infinitely often -- every instant, rather than daily or monthly. No real bank account compounds truly continuously, but it's a useful upper bound: as this calculator's own comparison table shows, continuous compounding adds only a tiny sliver of yield beyond daily compounding, so real-world accounts rarely have much room left to gain from compounding even more often.
How is this different from the Compound Interest Calculator?
This calculator answers a narrower question -- for a single year, what does a given nominal rate and compounding schedule actually yield? The Compound Interest Calculator instead projects a starting balance (plus optional ongoing contributions) forward over many years to show how it grows over time. Use this one first to find the real yield, then use Compound Interest to see what that yield does to a balance over the long run.
What is the difference between APY and APR?
APY (Annual Percentage Yield) describes what a deposit account -- a savings account or CD -- actually EARNS you in a year, factoring in compounding. APR (Annual Percentage Rate) describes what a loan or credit product COSTS you to borrow. They use related math (both account for compounding effects), but apply to opposite sides of a transaction, so they're never directly interchangeable.
Does a higher advertised APY always mean a better account?
Not necessarily -- APY reflects the current rate only and doesn't account for account fees, minimum-balance requirements, or whether the advertised rate is a temporary promotional rate that drops after an introductory period. Check the full terms, not just the headline APY, before comparing accounts.
Can APY ever be lower than the nominal rate?
No -- with a positive interest rate, APY is always equal to or higher than the nominal rate, never lower. It equals the nominal rate only in the special case of annual compounding (once per year); any more frequent compounding pushes APY strictly above it.
Does APY apply to loans as well as savings accounts?
The same compounding math applies, but the terminology is reversed by convention -- for a deposit account you earn APY, while for a loan the equivalent compounding-adjusted figure is folded into the APR instead. Use the Annual Percentage Rate (APR) Calculator for a loan, and this calculator for a deposit or savings account.
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