Accrued Interest Calculation Formula and Example

The accrued interest formula for simple interest is I = P × r × t, where principal is multiplied by the annual interest rate and the fraction of a year that has passed. This calculator estimates accrued interest from a principal amount, an annual rate, and elapsed days, using a 365-day year; it also shows the daily accrual and total amount including interest.

Formula

For simple interest calculated on an actual/365 basis, use:

I = P × (APR ÷ 100) × (d ÷ 365)

• I is accrued interest in dollars.
• P is the principal on which interest accrues, in dollars.
• APR is the annual interest rate entered as a percentage, such as 6 for 6%.
• d is the number of elapsed days.

The calculator’s daily accrual is P × (APR ÷ 100) ÷ 365. Its total is principal plus the calculated interest. The rate is divided by 100 to turn a percentage into a decimal; dividing annual interest by 365 converts the annual amount to an estimated daily amount. This is a simple-interest calculation: it does not add previously accrued interest to the principal during the period.

Worked Example

Using the calculator’s defaults—$10,000 principal, 6% annual interest, and 90 days—first convert the rate to decimal form: 6 ÷ 100 = 0.06. Then apply the actual/365 formula:

1. Annual simple interest: $10,000 × 0.06 = $600.
2. Accrued interest for 90 days: $600 × 90 ÷ 365 = $147.9452….
3. Rounded to cents, accrued interest is $147.95.
4. Daily accrual: $600 ÷ 365 = $1.6438 per day, displayed to four decimal places.
5. Principal plus accrued interest: $10,000 + $147.95 = $10,147.95.

The result uses the exact formula before rounding the interest output to cents. The total output adds the unrounded formula result to principal and then displays the total to cents, so it may differ by one cent from adding separately rounded display values in other cases.

Assumptions

• The annual rate is fixed throughout the entered period.
• The calculation treats interest as accruing day by day on the stated principal, with no interim payments.
• The day-count basis is 365 days, including in a leap year; it is not an actual/366 or 30/360 calculation.
• Interest is simple, not compounded during the period. Fees, taxes, payments, and lender-specific adjustments are not included.

What Accrued Interest Means

Accrued interest is interest that has accumulated over time but has not necessarily been paid or posted to an account yet. It is a time-based amount: with principal and rate unchanged, more elapsed days generally produce more accrued simple interest. The figure can appear in loan payoff calculations, bond transactions, savings or deposit account records, and other settings where interest accumulates between payment or posting dates.

“Accrued” does not always mean “compounded.” Simple interest is calculated only on the original principal for the interval. Compound interest, by contrast, can add interest to the balance, so future interest is calculated on a larger amount. A product may also calculate interest daily and post it monthly, or apply other contract-specific conventions. The label alone does not determine the method.

Day-Count Methods and Compounding

The 365-day denominator is an explicit assumption, not a universal rule. Financial agreements and instruments may use actual days over 360 days, actual days over 365 days, a 30/360 convention, or another defined method. Those conventions can produce different amounts from the same principal, rate, and calendar dates. A leap year does not automatically mean a 366-day denominator; follow the stated agreement or account method.

For an actual/360 example, replace 365 in the formula with 360. For a 30/360 convention, the number of days is determined using that convention’s date rules rather than simply counting calendar days. Compounding also changes the calculation. If interest is compounded periodically, the balance grows according to the compounding schedule, and a single simple-interest multiplication may not match the account’s accrued balance.

When accuracy matters, check the relevant statement, contract, transaction confirmation, or lender disclosure for the day-count basis, compounding frequency, rate definition, and dates used. This calculator is a transparent estimate under one stated convention, not a substitute for those terms.

How to Use and Read the Calculator

• Enter the principal amount on which interest is actually accruing, not automatically the original amount borrowed if the balance has changed.
• Enter the annual rate as a percentage. For example, type 6 for 6%, not 0.06.
• Enter the number of elapsed days in the period. For date-based accuracy, confirm which start and end dates count as accrual days under the applicable terms.
• Read accrued interest as the estimated interest for that interval; the daily figure helps show the approximate change for each additional day when the inputs stay constant.

The principal-plus-interest output is only the sum of the entered principal and this interval’s simple interest. It is not automatically a payoff quote or account balance: other payments, charges, accrued amounts from earlier periods, and contract rules may affect those figures.

Common Errors and Limits

A frequent mistake is entering a percentage in decimal form. In this calculator, 6 means 6%; entering 0.06 means 0.06%, one hundredth as large. Another is confusing days with months: enter the number of days, not 3 for a three-month interval. If the interval spans calendar months, count days according to the applicable method rather than assuming every month has the same length.

Also check whether the entered principal is the balance that earns interest during the period. Payments, withdrawals, rate changes, and compounding can make a single fixed-principal estimate inaccurate. Rounding can create small differences too: calculations may retain fractions of a cent internally, while statements can round daily, monthly, or at another stage. The displayed result is an estimate under the assumptions above, not a promise of the posted amount.

Frequently Asked Questions

How do I calculate accrued interest?
For simple interest on an actual/365 basis, multiply principal by the annual rate as a decimal, then multiply by days accrued and divide by 365: I = P × (APR ÷ 100) × d ÷ 365.

Is accrued interest the same as compound interest?
No. Accrued interest is interest accumulated but not necessarily paid or posted. Compound interest specifically involves calculating later interest on a balance that includes previously added interest.

Why does my accrued interest differ from this estimate?
The account may use a different day-count convention, compounding schedule, balance, rate, or rounding method. Payments or rate changes during the period can also change the result.

Do I use 365 or 360 to calculate accrued interest?
Use the day-count basis stated in the applicable terms. This calculator uses 365; some calculations use 360 or a date convention such as 30/360, so the same inputs can yield a different amount.

Does accrued interest increase the amount I owe?
It can be part of an amount due or a balance, depending on the account’s terms and how interest is posted. This estimate only adds the calculated interval’s interest to the entered principal; it does not model a specific account or payoff amount.

This result is an estimate for educational arithmetic, and the lender’s disclosure gives the exact figures.

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in p | Principal | $ | 10000 | 0.01 | 100000000
in apr | Annual interest rate | % | 6 | 0.01 | 100
in days | Days accrued | days | 90 | 0 | 36500
out int | Accrued interest | $ | p * (apr / 100) * days / 365 | 2
out daily | Interest per day | $ | p * (apr / 100) / 365 | 4
out total | Principal plus accrued interest | $ | p + int | 2