APY Calculator

APY is evaluated from Nominal Rate and Compounding Frequency. The calculation reports APY and APY - APR Difference.

Results

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About the APY Calculator

APY is treated here as a quantitative relation between Nominal Rate and Compounding Frequency and APY and APY - APR Difference.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
APY = (1 + APR / n)^n - 1
- APR = nominal annual rate (as a decimal)
- n = number of compounding periods per year
(365 = daily, 12 = monthly, 4 = quarterly, 2 = semi-annual, 1 = annual)
To convert APY back to APR:
APR = n x [(1 + APY)^(1/n) - 1]

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

APY = (1 + APR / n)^n - 1
- APR = nominal annual rate (as a decimal)
- n = number of compounding periods per year
(365 = daily, 12 = monthly, 4 = quarterly, 2 = semi-annual, 1 = annual)
To convert APY back to APR:
APR = n x [(1 + APY)^(1/n) - 1]

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: High-Yield Savings Account

Inputs

apr: 4.75 compounding: 365
APY: 4.8643%. APY - APR Difference: 0.1143%

With Nominal Rate = 4.75 and Compounding Frequency = 365 as the stated inputs, the result is APY = 4.8643% and APY - APR Difference = 0.1143%. Each value corresponds to the declared output fields.

Example 2: 1-Year CD — Monthly Compounding

Inputs

apr: 5.25 compounding: 12
APY: 5.3782%. APY - APR Difference: 0.1282%

With Nominal Rate = 5.25 and Compounding Frequency = 12 as the stated inputs, the result is APY = 5.3782% and APY - APR Difference = 0.1282%. Each value corresponds to the declared output fields.

Example 3: Credit Card Daily Compounding

Inputs

apr: 24.99 compounding: 365
APY: 28.3787%. APY - APR Difference: 3.3887%

With Nominal Rate = 24.99 and Compounding Frequency = 365 as the stated inputs, the result is APY = 28.3787% and APY - APR Difference = 3.3887%. Each value corresponds to the declared output fields.

Example 4: Annual vs Monthly Compounding Comparison

Inputs

apr: 6 compounding: 12
APY: 6.1678%. APY - APR Difference: 0.1678%

With Nominal Rate = 6 and Compounding Frequency = 12 as the stated inputs, the result is APY = 6.1678% and APY - APR Difference = 0.1678%. Each value corresponds to the declared output fields.

Common Use Cases

  • Convert a savings account APR to APY to compare with other accounts
  • Find the true effective yield of a CD or high-yield savings account
  • Compare two accounts with different compounding frequencies