Accrued Interest Formula and Calculator

The accrued interest formula is Interest = Principal × Annual rate × Time, adjusted for the day-count convention and compounding stated in the agreement. This calculator estimates simple accrued interest between two dates: enter the principal, annual rate, and elapsed days, then it returns the interest accrued and the principal-plus-interest amount.

Formula

For simple interest, the formula is I = P × r × d / B. Here, I is accrued interest in dollars, P is principal in dollars, r is the annual interest rate as a decimal, d is the number of accrued days, and B is the selected day-count denominator: 365, 360, or 360 in this calculator’s 30/360 option. The calculator accepts the rate as a percentage, so it uses apr / 100 in place of r. The second output is P + I.

In Actual/365 and Actual/360, d represents the actual number of elapsed calendar days, while the denominator is 365 or 360. In 30/360, a financial convention treats each month as 30 days and the year as 360 days. The selector here uses the number of days you enter; it does not convert start and end dates into convention-adjusted days.

Worked Example

Using the defaults—$20,000 principal, an 8% annual rate, 90 days, and Actual/365—the calculation is:

1. Convert the annual percentage to a decimal: 8 / 100 = 0.08.
2. Calculate the year fraction: 90 / 365 = 0.24657534.
3. Multiply principal by rate and year fraction: $20,000 × 0.08 × 90 / 365 = $394.5205.
4. Round the accrued interest to cents: $394.52.
5. Add it to principal: $20,000 + $394.52 = $20,394.52.

Assumptions

• The rate is fixed over the accrued period and is entered as an annual percentage.
• This is simple interest, not interest-on-interest; it does not add accrued interest to principal during the period.
• The input is the number of days applicable to the selected day-count convention. Payments, rate changes, and date-boundary rules are not modelled.
• No fees, taxes, insurance, or other charges are included.

What Accrued Interest Means

Accrued interest is interest that has accumulated over time but has not yet been paid or, in some settings, posted to an account. It describes an amount earned or owed through a particular date—not necessarily the amount due immediately. A loan statement may show accrued interest separately from principal, while an investment or account may show it as earnings not yet paid out.

The basic formula works by finding the portion of a year represented by the accrual period, then applying the annual rate to the principal for that portion. For instance, a 90-day period is not automatically one quarter of a year: under Actual/365 it is 90/365, while under a 30/360 convention a quarter-year is commonly represented as 90/360. The difference affects the result.

The calculator’s principal-plus-interest figure is an arithmetic subtotal, not a payoff quote or account balance forecast. A real account can include payments, daily balance changes, fees, rounding rules, or compounding. Check the contract or account statement for the applicable method and exact amount.

Choosing a Day-Count Method

The day-count convention specifies how a year fraction is calculated. It is set by the instrument or agreement, not chosen just to obtain a preferred result. Common labels include Actual/365, Actual/360, and 30/360, but specific contracts can define details differently.

• Actual/365: Uses actual calendar days and a 365-day denominator. The denominator stays 365 in this calculator, including for periods that cross a leap day.
• Actual/360: Uses actual calendar days and a 360-day denominator. With the same principal, annual rate, and days, this produces more simple accrued interest than Actual/365 because the denominator is smaller.
• 30/360: Uses a 360-day year built from twelve 30-day months. Actual convention rules may adjust how month-end dates are counted; this calculator does not apply those adjustments automatically.

To use the calculator for dates, first determine the day count under the agreement’s rule, then enter that count and select the corresponding basis. If a contract specifies another method, such as an Actual/Actual variant, this calculator’s options may not reproduce it exactly.

Simple Interest, Compounding, and Common Errors

This formula assumes simple interest on an unchanged principal. With compounding, previously accumulated interest can itself earn interest, so the simple formula may understate the amount over longer periods. A compounding calculation needs the compounding frequency and the exact timing rules; do not treat this calculator’s output as a compounded balance.

Common sources of a mismatch include:

• Using the wrong rate format: Enter 8 for 8%, not 0.08. The calculator converts the percentage to a decimal.
• Mixing day conventions: Actual/360 and Actual/365 use different denominators; the agreement determines which applies.
• Counting dates differently: Whether the start date, end date, or both are included can change the day count. Follow the relevant account rule.
• Confusing accrued interest with total interest: Accrued interest covers the entered period only. It is not necessarily all interest over a loan’s life.
• Rounding at different stages: The calculator rounds the interest result to cents. A provider may calculate with more decimal places or round daily, creating a small difference.

For a changing principal, such as a loan with payments during the period, one calculation using the original principal will not represent each day’s balance. The period may need to be split into segments with the correct balance and rate for each segment.

Frequently Asked Questions

How do I calculate accrued interest?
Multiply principal by the annual rate as a decimal and by the applicable fraction of a year: I = P × r × d / B for a simple-interest calculation. Confirm the day-count basis first.

Is accrued interest calculated daily?
It can be. A daily accrual method applies an annual rate to a daily balance using a stated day-count denominator. This calculator estimates the total for the full period from the entered principal and day count; it does not model daily balance changes.

Why does Actual/360 give a different result from Actual/365?
For the same actual days, principal, and rate, dividing by 360 creates a larger year fraction than dividing by 365. The applicable convention depends on the agreement.

Does accrued interest include compounding?
Not in this calculator. It uses simple interest on the entered principal. A compounded balance requires a formula that accounts for how often interest is added to principal.

Is accrued interest the amount I must pay?
Not necessarily. It is interest accumulated through a specified date under the stated assumptions. A payment or payoff amount can also depend on the current principal, transaction timing, contract terms, and other charges.

This result is an estimate; the lender’s disclosure gives the exact figures.

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in p | Principal | $ | 20000 | 0 | 100000000
in apr | Annual interest rate | % | 8 | 0.01 | 100
in days | Days accrued | days | 90 | 0 | 36500
sel basis | Day-count basis | Actual/365=365, Actual/360=360, 30/360=360
out int | Accrued interest | $ | p * (apr / 100) * days / basis | 2
out total | Principal plus accrued interest | $ | p + int | 2