Reference formulas and worked examples below keep their stated units. Monetary examples use USD; dimensional examples use US customary units unless labeled otherwise. Metric calculator inputs are converted to these reference units before calculation. Choosing another currency does not convert example amounts or exchange money.
How to use this apy calculator
Select a compounding frequency. The conversion assumes a constant rate with interest left in the account; it is not a borrowing-fee APR calculation.
How the calculation works
For nominal annual rate j and n compounding periods per year, APY = (1 + j/n)^n − 1. Reverse it with j = n × [(1 + APY)^(1/n) − 1]. Rates in these formulas are decimal values.
For continuous compounding, APY = exp(j) − 1, and the inverse nominal rate is ln(1 + APY). Continuous compounding is a mathematical model, not a claim about an actual account.
Example ending balance = starting deposit × (1 + APY)^years. Fractional years use the same geometric growth assumption. Interest earned is ending balance minus deposit, with money rounded only for display.
A deposit APY reflects interest and compounding. Borrowing APR can include finance charges and is a different calculation; this tool does not translate a fee-bearing loan APR into a deposit yield.
Worked example
A 12% nominal annual rate compounded monthly has 1% growth per month. Its APY is (1.01^12 − 1) × 100 = about 12.6825%. A 1,000 deposit becomes 1,126.83 after one year. Reversing that APY with monthly compounding returns 12% nominal.
Limits and assumptions
A constant-rate mathematical model, not a product quote or a regulated APY disclosure for an actual account. No account fees, taxes, tiered balances, promotional rates, deposits, withdrawals, leap-year calendars or early-withdrawal terms. Negative rates represent hypothetical shrinking balances. Extreme projections are rejected rather than displayed as Infinity.
Frequently asked questions
Is APY the same as the nominal annual interest rate?
Only when the chosen compounding convention makes them equal, such as one annual compounding period. More frequent compounding changes the effective annual result.
Can I work backward from APY?
Yes. Select the reverse direction and choose the same compounding frequency used by the nominal rate you want to find.
What is continuous compounding?
It is the mathematical limit as interest is compounded more and more frequently. The formula uses an exponential, not a finite number of crediting dates.
Can I use a loan’s advertised APR as this input?
Not as a fee-aware loan analysis. This converter assumes a pure nominal interest rate or an effective deposit yield. Use the borrowing APR tool for loan cash flows.
Does changing currency apply an exchange rate?
No. It only chooses the currency of the illustrative deposit amounts.