Accrued Interest Calculator: Formula and Example

An accrued interest calculator estimates the interest that has accumulated on a loan or other debt over a stated number of days, based on its balance, annual rate, and day-count convention. Enter the principal, annual interest rate, elapsed days, and days in the year; the result is an estimate of interest accrued during that period.

Formula

This calculator uses simple interest on a constant principal balance:

Accrued interest = principal × (annual rate ÷ 100) × (elapsed days ÷ days in year)

• Principal (p): the balance on which interest accrues, in dollars.
• Annual interest rate (apr): the annual rate entered as a percentage, such as 8 for 8%.
• Days accrued (days): the period being estimated, measured in days.
• Days in year (year): the denominator used for the day-count calculation, commonly 365 or 360 depending on the contract and product.
• Accrued interest (interest): the estimated amount in dollars, rounded to cents.
• Balance including accrued interest (total): principal plus the calculated interest; it does not include fees or other charges.

The calculator treats the annual rate as a decimal by dividing it by 100. It then applies the fraction of a year represented by the elapsed days. This is a simple-interest estimate, not a compounding schedule. The result is not necessarily the amount due on a particular date: the contract may specify another method, payment timing, or rounding rule.

Worked Example

Using the calculator’s default values—$20,000 principal, 8% annual interest, 30 days, and a 365-day year:

1. Convert the rate to a decimal: 8 ÷ 100 = 0.08.
2. Find the portion of the year: 30 ÷ 365 ≈ 0.08219178.
3. Multiply: $20,000 × 0.08 × (30 ÷ 365) ≈ $131.5068.
4. Round the accrued interest to cents: $131.51.
5. Add it to principal: $20,000 + $131.51 = $20,131.51.

Calculations made with unrounded intermediate values can differ by a fraction of a cent from calculations that round interest daily or monthly. The calculator rounds its displayed interest to two decimal places.

Assumptions

• The principal remains unchanged throughout the period. Payments, new borrowing, or balance adjustments are not modelled.
• The stated annual rate is fixed for the entire elapsed period.
• Interest is estimated as simple interest, with no additional compounding during the period.
• The entered days-in-year value determines the day-count basis; use the convention specified by the account or contract.
• Payment timing, fees, taxes, insurance, and other charges are not included.

When Accrued Interest Matters

Accrued interest is interest that has accumulated since the last date on which interest was settled, posted, or paid. It can help explain why a payoff quote or account balance differs from the principal alone. For example, a borrower may make a payment after several days have passed since the previous payment; interest may have accumulated in the meantime.

The same general idea applies to interest-bearing investments: interest can build between payment dates. However, this calculator’s formula is for a constant principal and simple daily accrual. Bonds and other securities can have specific settlement conventions, coupon schedules, and market-price calculations. Use the instrument’s stated method rather than assuming this estimate is its official accrued-interest figure.

To use the calculator, identify the balance that actually accrues interest, the applicable annual rate, the number of days in the period, and the contract’s year basis. If the balance or rate changed during the period, calculate each segment separately and add the results, using the correct balance and rate for each segment.

Day-Count Methods and Compounding

A year does not always mean 365 days in an interest calculation. Some agreements use a 360-day denominator; others use 365, 366 in a leap-year period, or a specified method that treats calendar months differently. A 360-day basis produces a larger simple-interest estimate than a 365-day basis for the same principal, rate, and number of days. The contract or account statement is the source for which convention applies.

Compounding is another separate issue. With simple interest, the calculation applies the rate to the original principal. With compounding, previously accumulated interest can itself earn interest after it is added to the balance. A compound-interest calculation needs the compounding frequency and timing, and may not match a daily-accrual figure on a statement. Do not select a day-count denominator merely because it produces a result that looks familiar.

Common Mistakes and Limits

• Entering 0.08 instead of 8: the rate field expects a percentage, so enter 8 for 8%.
• Using the wrong balance: use the balance that accrues interest, not automatically the original amount borrowed if principal has since been paid down.
• Counting days incorrectly: the start and end dates may be included or excluded according to the agreement. Confirm the applicable rule before choosing the elapsed-day count.
• Assuming all lenders use 365 days: the calculation’s result changes with the denominator. Check the loan documents or statement.
• Confusing accrued interest with the amount due: a payoff or payment amount can include principal, fees, penalties, or other items that this calculator does not model.
• Ignoring balance changes: if a payment or rate change occurred during the period, one calculation using a single balance and rate may be inaccurate.

The calculator is therefore most useful as a transparent arithmetic estimate, not as a substitute for a contractual balance or payoff figure. For an exact amount, use the method and dates supplied by the account provider or obtain a current statement.

Frequently Asked Questions

How do I calculate accrued interest?
Multiply the principal by the annual rate as a decimal, then multiply by elapsed days divided by the applicable days-in-year figure. For example, $20,000 at 8% for 30 days on a 365-day basis gives about $131.51.

Is accrued interest the same as principal?
No. Principal is the amount owed or invested before adding interest. Accrued interest is the interest accumulated over a period. A simple combined balance is principal plus accrued interest, though an actual account balance may include other items.

Should I use 360 or 365 days?
Use the day-count convention stated in the loan or account terms. The calculator does not determine which convention applies, and choosing a different denominator changes the result.

Does accrued interest compound?
Not in this calculator. It estimates simple interest on an unchanged principal. Whether interest compounds, and how often, depends on the account’s terms and requires a different calculation when applicable.

Why is the calculator’s result different from my statement?
Possible reasons include a different balance, day-count method, start or end date, daily rounding, compounding, payments, or fees. Compare the statement’s dates and calculation convention with the inputs.

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

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in p | Principal balance | $ | 20000 | 0 | 100000000
in apr | Annual interest rate | % | 8 | 0.01 | 100
in days | Days accrued | days | 30 | 0 | 366
in year | Days in year | days | 365 | 1 | 366
out interest | Accrued interest | $ | p * (apr / 100) * days / year | 2
out total | Balance including accrued interest | $ | p + interest | 2