Calculate prorated (pro rata) interest from the balance, annual rate and number of days or two dates, or solve for the principal, rate or days.
Prorated Interest Formula
For the default 365-day denominator, the following equation estimates prorated simple interest. Replace 365 with the selected 360- or 366-day denominator when appropriate; the annual rate R in this article is a decimal.
- Where PI is the prorated interest ($)
- P is the principal ($)
- R is the annual interest rate (decimal)
- D is the number of days in the partial period
To estimate prorated interest, multiply the principal by the daily simple interest rate (decimal annual rate divided by the selected year denominator), then multiply by the counted days. Enter a percentage such as 5, not 0.05, in the calculator’s annual-rate field. A fixed 366 denominator does not implement every Actual/Actual convention, and this tool does not derive 30/360 calendar-day adjustments.
What is Prorated Interest?
Definition:
Prorated interest refers to the portion of interest owed on a loan or investment for a fraction of the total annual period. It is commonly used when an account is opened or closed mid-cycle, or when balancing partial months or days within a billing or investment timeframe.
How to Calculate Prorated Interest?
Example Problem:
The following example outlines the steps and information needed to calculate the Prorated Interest.
First, determine the principal. In this example, the principal is $5,000.
Next, determine the annual interest rate. In this example, the annual interest rate is 5% (0.05 in decimal form).
Then, determine the partial period in days. Suppose the partial period is 15 counted days and select the default 365-day denominator.
Finally, calculate the prorated interest using the formula above:
PI = P * (R / 365) * D
PI = 5000 * (0.05 / 365) * 15
PI = $10.27 in interest (approximately)
FAQ
Does this formula account for compounding?
This simple prorated interest formula assumes simple interest and does not include compounding. If compounding applies, you may need a different formula or calculator that takes into account the compounding frequency.
Can I use months instead of days in the calculation?
This calculator accepts counted days. Use your agreement’s day-count method rather than assuming every month has 30 days or 365/12 days. A monthly simple-interest convention is a different calculation.
What if the partial period crosses multiple billing cycles?
If the partial period spans multiple billing cycles, you may need to split your calculation or use an average daily balance method. The same basic concept applies, but each portion of the timeframe might have different balance amounts or interest rates.
