Savings & interest
APY and interest rate
Convert a nominal annual interest rate to APY, or annualize interest earned on an unchanged principal over a supplied number of days.
Your inputs
Complete the fields for your selected method. Zero means intentionally zero, not unknown. Currency selection labels amounts; it does not convert exchange rates.
How this calculation works
nominal-rate APY = (1 + rate / periods) ^ periods - 1; earned-interest APY = (1 + interest / principal) ^ (365 / days) - 1
Nonnegative rates and interest only. The earned-interest method assumes unchanged principal, no contributions or withdrawals, and that entered interest matches that principal and period. Variable rates, tiered balances, fees and special account terms can require different disclosure calculations. This is educational arithmetic, not a compliance certification or investment recommendation.
What information do I need?
Use records for the same job, equipment or accounting period. Only the fields for your selected entry method are required. An unknown amount is not zero.
Input definitions and where to find them
- Which information do you have?: Use matching records or an explicitly identified assumption for which information do you have?. Unknown is not the same as zero.
- Nominal annual interest rate (%): Use matching records or an explicitly identified assumption for nominal annual interest rate. Unknown is not the same as zero. Used with: Nominal annual rate and compounding frequency.
- Compounding frequency for the nominal interest rate: Use matching records or an explicitly identified assumption for compounding frequency for the nominal interest rate. Unknown is not the same as zero. Used with: Nominal annual rate and compounding frequency.
- Unchanged principal on deposit (selected currency): Use matching records or an explicitly identified assumption for unchanged principal on deposit. Unknown is not the same as zero. Used with: Principal, interest earned and days.
- Interest earned, excluding deposits (selected currency): Use matching records or an explicitly identified assumption for interest earned, excluding deposits. Unknown is not the same as zero. Used with: Principal, interest earned and days.
- Days in the earnings period (days): Use matching records or an explicitly identified assumption for days in the earnings period. Unknown is not the same as zero. Used with: Principal, interest earned and days.
Use the Where to find this value controls beside the inputs for available work-it-out helpers. Estimates remain your assumptions; a helper does not verify the source figures.
Worked example
Example amounts use US dollars (USD).
Example answer: Calculated annual percentage yield is 4.080849 % for the illustrative inputs below.
Example inputs
- Which information do you have?: Nominal annual rate and compounding frequency
- Nominal annual interest rate: 4.00 %
- Compounding frequency for the nominal interest rate: Daily (365 periods per year)
- Calculated annual percentage yield
- 4.080849 %
- Illustrative one-year interest per 1,000 deposited
- $40.81
- Annualizing a short observation does not predict future earnings. Rates are supplied, not current bank offers. The 1,000-unit illustration uses the selected currency label.
These illustrative values are not recommended rates or industry averages. Replace every example input with your own figures.
Use the result well
Convert a nominal annual interest rate to APY, or annualize interest earned on an unchanged principal over a supplied number of days.
Keep inputs on the same scope and time basis. Calculations retain precision internally; displayed values generally round to two decimal places, with extra precision for very small values and whole-unit rounding where required. Economic comparisons describe your supplied assumptions and do not guarantee future results.
This tool provides business arithmetic. It does not approve engineering designs, establish legal or tax treatment, select equipment or certify safe operating conditions.