Accrued Interest Calculation: Formula and Examples

An accrued interest calculation estimates the interest earned on an investment or owed on a loan between interest payment dates. Enter the principal, annual rate, and elapsed days to calculate simple accrued interest; the result does not include fees or compounding unless the contract’s method requires them.

Formula

For simple interest using a stated day-count basis, accrued interest equals principal multiplied by the annual interest rate, multiplied by the fraction of a year elapsed:

I = P × (r / 100) × (d / B)

• I is accrued interest, in dollars.
• P is the principal or balance on which interest accrues, in dollars.
• r is the annual rate, entered as a percentage.
• d is the number of accrued days.
• B is the day-count basis: the number of days treated as one year for this calculation.

The second output, P + I, is the principal plus the calculated interest. It is not necessarily the payoff amount: a lender or investment contract may use a different accrual convention, add charges, or account for payments and compounding.

Worked Example

Using the calculator’s default inputs—$20,000 principal, an 8% annual rate, 30 days, and a 365-day basis:

1. Convert the annual percentage to a decimal: 8 / 100 = 0.08.
2. Find the year fraction: 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.

What Accrued Interest Means

Interest can accumulate continuously over time even when it is paid only monthly, quarterly, semiannually, or at maturity. The amount accumulated since the last payment or accounting date is accrued interest. It is a time-based amount, not necessarily a separate fee, and its treatment depends on the instrument’s terms and accounting method.

For a loan, interest generally accrues on an outstanding balance; payments may reduce that balance and affect later accrual. For a bond or other interest-paying investment, interest may accrue between coupon dates. In a transaction between coupon dates, the buyer may pay the seller accrued interest along with the agreed price, then receive the next scheduled coupon. The precise settlement calculation depends on the security’s terms and market convention.

Day-Count Methods and Compounding

The calculator uses a straightforward actual-days-over-a-chosen-year approach. The numerator is the actual number of days entered, while the denominator is the selected basis. A 365-day basis and a 360-day basis produce different results for the same principal, rate, and elapsed days. Some contracts instead use methods that treat months as equal lengths or adjust the year length; the correct method is specified by the contract or instrument documentation.

This calculator assumes simple accrual across the entered period. It does not add interest to principal during that period. If interest compounds, the calculation must account for the compounding frequency. For example, a nominal annual rate compounded several times per year is not identical to multiplying principal by the annual rate and a simple fraction of a year. Do not substitute a day-count convention or compounding method based on guesswork.

How to Use and Interpret the Result

• Enter the principal or balance that actually accrues interest during the period.
• Enter the annual rate as a percentage: 8 means 8%, not 0.08%.
• Enter the number of accrued days and the day-count basis required by the relevant terms.
• Read the first result as interest for that period, rounded to cents; the second adds that amount to the starting principal.

For an estimate spanning a payment or balance change, calculate separate periods using the applicable balance for each one. A single calculation using the original principal may overstate interest if payments reduced the balance during the period. Likewise, if the rate changes, divide the timeline into the periods with their respective rates.

Common Errors and Limits

A frequent mistake is confusing the annual rate with the rate for the elapsed period. At 8% annually, 30 days does not normally mean charging 8% of principal; the day fraction scales the annual rate. Another error is choosing 360 or 365 without checking the governing convention. Even a small convention difference changes the result, especially for larger balances or longer periods.

The arithmetic here is not a statement of what a lender or issuer will charge, credit, or require at settlement. The input rate must match the relevant contract and may not be interchangeable with an advertised APR or yield. APR can incorporate features beyond the interest accrual rate, while some instruments use compounding, variable rates, payment histories, or specialized day-count rules. This calculator also does not model fees, taxes, late charges, missed payments, or adjustments.

Frequently Asked Questions

How do I calculate accrued interest?
For simple interest, multiply principal by the annual rate expressed as a decimal, then by elapsed days divided by the applicable day-count basis: I = P × (r / 100) × (d / B).

Is accrued interest the same as interest paid?
No. Accrued interest is the amount built up over a period. It may be paid on a later scheduled date, included in a settlement calculation, or recorded before cash changes hands.

Should I use 360 or 365 days?
Use the basis required by the loan, security, or agreement. The answer is not universal; different conventions can yield different accrued amounts.

Does accrued interest include compounding?
Not in this calculator. It uses simple interest for the selected period. If the applicable terms compound interest, use a formula that reflects the compounding schedule.

Why might my lender’s amount differ?
The lender may use a different day-count convention, balance, rate, accrual dates, payment timing, rounding rule, or compounding method. Check the contract or ask the lender how it calculated the figure.

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 | 30 | 0 | 366
in basis | Days in year | days | 365 | 1 | 366
out acc | Accrued interest | $ | p * (apr / 100) * days / basis | 2
out total | Principal plus accrued interest | $ | p + acc | 2