How to Calculate Rate per Period
Understanding the periodic rate is fundamental in mathematics, finance, and physics when dealing with exponential growth, decay, or compounding cycles. This calculator helps you determine the rate applied for a specific time segment based on a nominal annual value.
Please enter a valid numeric rate.
What is Rate per Period?
The Rate per Period (often denoted as i) represents the percentage of interest, growth, or decay that is applied at the end of a single compounding interval. While annual rates (APR or Nominal Rates) are the standard for quoting figures, calculations for amortization, compound interest, or biological growth often require the rate to be broken down into smaller time segments.
The Periodic Rate Formula
To calculate the rate per period, you divide the nominal annual rate by the number of compounding periods in one year.
- i = Rate per period
- r = Nominal annual rate (as a percentage or decimal)
- n = Number of compounding periods per year
Real-World Calculation Examples
Example 1: Monthly Compounding
Assume you have an annual nominal rate of 12% and the compounding frequency is monthly.
- r = 12%
- n = 12 (12 months in a year)
- Calculation: 12% / 12 = 1%
In this scenario, the rate per period is 1% per month.
Example 2: Daily Compounding
Consider a process with a 5% annual rate compounded daily.
- r = 5%
- n = 365
- Calculation: 5% / 365 ≈ 0.0137%
The rate applied every single day is approximately 0.0137%.
Why distinguish between Annual and Periodic Rates?
Mathematical models work on cycles. If a formula iterates 12 times a year, you cannot input the annual rate directly, or you would be calculating 12 years' worth of growth every month. You must scale the rate down to match the duration of the cycle (the period).
Common Periods (n)
- Daily: 365 or 360
- Weekly: 52
- Monthly: 12
- Quarterly: 4