Rate Per Period Calculator
Understanding the Rate Per Period
In finance and mathematics, the rate per period is the specific percentage applied to a principal balance during a single compounding interval. While most financial products are marketed using an annual percentage, the actual math used to calculate growth or debt usually happens on a much smaller scale, such as monthly or daily.
The Formula
Calculating the periodic rate is straightforward. It is the quotient of the nominal annual rate divided by the frequency of intervals in a single year.
Where:
i = Rate per period
r = Nominal Annual Percentage Rate
n = Number of compounding periods per year
Why This Metric Matters
The rate per period is the "engine" behind compounding interest. If you have a credit card with a 24% annual rate, the bank does not wait until the end of the year to charge you 24%. Instead, they apply a periodic rate (usually daily or monthly) to your balance. Knowing this rate helps you understand exactly how much "weight" each interval adds to your total balance.
Common Interval Frequencies
Depending on the context, the number of periods (n) changes:
- Monthly: n = 12 (Common for mortgages and car loans)
- Quarterly: n = 4 (Common for investment dividends)
- Semiannually: n = 2 (Common for bond coupon payments)
- Daily: n = 365 (Common for savings accounts and credit cards)
Step-by-Step Calculation Example
Imagine you have an investment that offers a 6% stated annual rate, compounded quarterly.
- Identify the annual rate: 6% (or 0.06 as a decimal).
- Identify the periods per year: Quarterly = 4.
- Divide the rate by the periods: 6 / 4 = 1.5%.
- Result: Your rate per period is 1.5% every three months.
Difference Between Periodic Rate and EAR
It is important not to confuse the periodic rate with the Effective Annual Rate (EAR). The periodic rate is a simple division, whereas the EAR accounts for the effect of compounding over the course of the whole year, showing the true annual cost or yield. The periodic rate is the input used to find the EAR.