5% nominal rate
100 × [(1 + 0.05 ÷ 12)¹² − 1]
The APY is approximately 5.11619%. The one-year growth factor is approximately 1.051161898. Before any fees or period-by-period rounding, 1,000 grows to about 1,051.161898 in this model.
One year of compound growth
APY Calculator
Convert between a nominal annual interest rate and APY, or use a known APY to find one-year interest and the ending balance.
Calculate APY, nominal rate, or one-year interest
Annual percentage yield (APY)
Enter the known rate and choose a compounding frequency, then select Calculate.
- Nominal annual interest rate
- Annual percentage yield
- Interest rate per period
- One-year growth factor
- Compounding frequency
- Starting balance
- Annual percentage yield
- Balance after one year
Assumes a constant APY for one full year, with all interest retained and no deposits, withdrawals, fees, or taxes. Amounts use the same unit as the starting balance.
≈ marks numerical approximation or display rounding. Calculations run in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations.
Worked examples
5% compounded twice a year
100 × (1.025² − 1) = 5.0625%
The period rate is exactly 2.5%, and the APY is exactly 5.0625%. Choosing annual compounding at the same nominal rate instead gives exactly 5% APY.
10.25% APY, twice a year
100 × 2 × (√1.1025 − 1) = 10%
A 10% nominal annual rate supplies 5% per period. Compounding those two periods gives 10.25% APY. An APY of 10.25% does not mean a 10.25% rate each period.
Already have a 5% APY?
APY already includes one year of compounding. In this model, a balance of 1,000 at 5% APY earns 50 over one year and ends at 1,050. This assumes the yield stays constant, all interest is retained, and there are no deposits, withdrawals, fees, or taxes. It is an illustration, not a quoted account return.
One-year interest = 1,000 × 5 ÷ 100 = 50
To calculate the amount for your own balance, select One-year interest from APY under Calculate and enter your starting balance and APY. For example, 10,000 at 3.25% APY earns 325 over one full year and ends at 10,325 under the same assumptions. This mode does not ask for compounding frequency because APY already includes the year's compounding effect.
One-year interest = starting balance × APY ÷ 100
Balance after one year = starting balance + one-year interest
To find the equivalent nominal rate for monthly compounding, select Nominal annual interest rate under Calculate, enter 5 in Annual percentage yield, and choose Monthly (12 periods). With six decimal places, the result is approximately 4.888949%. The APY stays 5%; the nominal rate describes how that yield is built up over the selected periods.
Entering 5 as the nominal rate with monthly compounding instead gives approximately 5.11619% APY, as in the example above. For a balance projection over several years or with regular deposits, use the Compound Interest Calculator. Its rate input is nominal, so convert a known APY using the same compounding frequency first; entering a rounded converted rate can slightly change the projection.
Formula, precision, and assumptions
APY = 100 × [(1 + R ÷ (100n))ⁿ − 1]
R is the nominal annual interest rate as an entered percentage, and n is the number of equal compounding periods per year. The rate per period is R ÷ n percent. The growth factor is 1 + APY ÷ 100. Reverse the formula to obtain R = 100n × [(1 + APY ÷ 100)^(1/n) − 1].
Both input rates are restricted to 0%–1,000%; negative rates are outside this calculator's scope. A computed APY can exceed 1,000%. The choices are 1, 2, 4, 12, or 365 equal periods. There is no continuous-compounding option or calendar-date calculation. For rate conversion, a zero input rate gives zero nominal rate, zero APY, and a growth factor of exactly 1.
Inputs allow up to 64 characters, 15 integer digits, and 10 decimal places, subject to the rate limit above. Forward calculations retain exact integer fractions. The inverse calculation detects exact rational roots; otherwise, it uses 120 significant digits and marks the solved rate with ≈.
One-year interest from APY accepts a nonnegative starting balance under the same numeric input limits and an APY from 0% to 1,000%. It multiplies the balance by APY ÷ 100 using exact fractions, then adds the unrounded interest to the starting balance. Zero APY earns zero interest; a zero balance remains zero. The displayed amounts can round independently, so their displayed sum may differ from the displayed ending balance. The precision setting changes display only, not how an account credits or rounds interest.
The selected maximum decimal places affect the final display only. Halfway values round away from zero, trailing zeros are removed, and ≈ also marks display rounding. A notice appears when a positive value rounds to zero. Changing precision does not add a history entry or change the underlying values.
These are mathematical calculations under a constant rate with no additional deposits or withdrawals. They do not predict or guarantee investment returns or calculate a product's regulatory APY disclosure. Actual accounts can have changing or tiered rates, different accrual and crediting rules, minimum balances, fees, taxes, and contractual rounding.
References: OpenStax — Compound Interest explains effective annual yield. The Consumer Financial Protection Bureau's compound-interest explanation describes interest earning further interest.
Common questions
How much does 3.25% APY earn on 10,000?
Select One-year interest from APY, enter 10,000 as the starting balance and 3.25 as the APY. The one-year interest is 325 and the ending balance is 10,325, assuming a constant yield, retained interest, and no deposits, withdrawals, fees, or taxes. Do not enter 3.25 as a nominal rate unless that is the rate you actually know.
Is APY the same as a nominal annual rate?
They are equal with annual compounding or a zero rate in this model. With a positive nominal rate and more frequent compounding, APY is higher because earlier interest earns more interest during the year.
Can I enter a loan APR as the nominal rate?
Use a stated nominal annual interest rate that matches the selected compounding frequency. A loan APR can reflect fees and other terms and is not interchangeable with this input. This calculator does not convert a regulated loan APR into an account yield.
Is APY a return over the entire investment period?
APY describes an effective yield for one year. A cumulative return over several years is a different quantity. This calculator does not annualize a return from start and end balances or calculate a money-weighted investment return.
What does daily compounding mean here?
The annual rate is divided into 365 equal periods, and interest is retained after each one. It does not account for a leap year, actual transaction dates, a 360-day basis, or a provider's separate accrual and crediting schedule.
Why does the reverse result show ≈?
Most nth roots are not exact finite decimals. The inverse calculation uses high-precision arithmetic and marks numerical approximations even when the displayed number looks simple. Exact rational roots, such as 10.25% APY compounded twice a year giving a 10% nominal rate, remain exact.