The formula
- P
- Principal or unpaid balance
- r
- Annual rate as a decimal
- B
- 360, 365, or 366 days
- d
- Number of accrued days
Worked example: $25,000 at 7.5% on a 365-day basis
Convert 7.5% to 0.075. The annual interest is $25,000 × 0.075 = $1,875. Divide by 365:
Rounded to cents, the daily interest is $5.14. For 45 days, the unrounded daily amount produces about $231.16 of simple interest.
How to calculate interest for several days
Once the daily interest is known, multiply it by the number of days: Interest = Daily interest × Days. Use the unrounded daily value for the calculation and round the final dollar result to cents unless the contract specifies a different rounding rule.
360 vs. 365 vs. 366 day interest
A smaller denominator produces more interest per day for the same principal and annual rate. A contract using Actual/360 therefore has a larger daily accrual than Actual/365. Leap-year calculations sometimes use 366, depending on the agreement or system.
Simple daily accrual is not daily compounding
This formula accrues simple interest on the stated principal. Daily compounding is different because each day's interest can become part of the balance used for the next day. Always match the calculation to the loan agreement or account rules.
Check the math with a calculator
Enter your own numbers in the matching Power of Interest calculator. The calculator performs the arithmetic while this page explains the formula and assumptions behind it.