Accrued Interest Calculator: Meaning and Formula

This calculator estimates accrued interest on a loan or deposit over a stated period, using a principal balance, annual interest rate, and number of days. Enter those figures and choose a day-count basis; the result is the interest accumulated before it is paid, posted, or added to the balance.

Formula

For a simple-interest estimate, accrued interest equals principal multiplied by the annual rate, multiplied by the elapsed days, and divided by the day-count basis:

I = P × (r / 100) × d / B

• I is accrued interest, in dollars.
• P is the principal balance on which interest accrues, in dollars.
• r is the annual interest rate, entered as a percentage.
• d is the number of days interest accrues.
• B is the number of days used as the year basis, usually 360 or 365 for simple day-based estimates. Some products use other conventions.

The second output is P + I: the principal plus the estimated accrued interest, assuming the interest has not been paid or otherwise applied. It is not necessarily the amount due on a statement, because fees, payment dates, compounding, and contract-specific rules may affect an actual balance.

Worked Example

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

1. Convert the rate to a decimal: 8 / 100 = 0.08.
2. Multiply principal by the annual rate: $20,000 × 0.08 = $1,600 per year.
3. Apply the fraction of the year: $1,600 × 30 / 365 = $131.5068…
4. Round the interest to cents: $131.51 accrued interest.
5. Add it to principal: $20,000 + $131.51 = $20,131.51.

This is a simple-interest estimate. It assumes the stated principal and rate remain unchanged throughout all 30 days.

What Accrued Interest Means

Accrued interest is interest that has accumulated over time but has not yet been paid, received, or necessarily recorded as a transaction. It describes an amount building between interest-payment or posting dates. The phrase applies on both sides of a financial arrangement: a borrower can owe accrued interest, while a saver or investor can have earned interest that has not yet been credited or paid.

Accrued does not automatically mean overdue. For example, a loan may accumulate interest each day while the borrower makes scheduled monthly payments. The interest accrues between payments, but it is not past due merely because it has accumulated. Whether it is payable, added to principal, or shown separately depends on the agreement and the timing of the account’s statements.

In bookkeeping, “accrued interest” may also refer to interest income earned or interest expense incurred but not yet settled in cash. The accounting entry and the cash payment date are distinct events. The calculator above focuses on estimating the amount over a span of days, not on accounting treatment.

How It Accumulates

With simple interest, the calculation uses the same principal for each day. If $20,000 accrues interest at 8% per year, the estimated daily amount on a 365-day basis is $20,000 × 0.08 / 365, or about $4.38. Over 30 days that is about $131.51, subject to rounding.

Some accounts instead compound interest: previously accumulated interest is added to the balance, and later interest may be calculated on that larger balance. A daily-compounding calculation is not identical to the simple-interest formula here. Payment products may also use a daily periodic rate, a changing balance, or a defined convention for counting the first and last day. Check the account terms or statement to learn which method applies.

For a changing loan balance, applying the formula to the original amount for a long period can overstate interest if payments reduce principal during that period. A more accurate calculation needs the balance over time, relevant payment dates, and the contract’s interest method.

Where Accrued Interest Appears

Common examples include loan statements, savings accounts, bonds, and transactions made between scheduled interest-payment dates. In a loan, unpaid interest can appear separately from principal; in a deposit or investment, earned interest may not become available until a crediting or payment date.

When a bond is bought between interest-payment dates, the buyer may pay the seller the interest that has accumulated since the previous payment date, in addition to the bond’s quoted price. The buyer then receives the next scheduled coupon under the bond’s terms. This accrued amount is different from the bond’s market price and from the total coupon payment. Bond conventions and settlement rules vary, so this simple calculator should not be treated as a bond-trading quote.

Day Counts, Rounding, and Common Mistakes

The day-count basis matters. Dividing by 365 gives a different estimate from dividing by 360, even with the same principal, rate, and elapsed days. The basis field lets you compare those arithmetic assumptions; it does not determine which convention a lender or investment uses. Some contracts specify how days are counted, including how leap years are handled.

• Enter the annual rate as a percentage: use 8 for 8%, not 0.08.
• Use the balance actually subject to interest, rather than automatically using the original amount borrowed.
• Count the accrual period correctly. A statement’s start and end dates may be treated according to the account’s own rules.
• Do not assume interest compounds just because it accrues daily. Accrual frequency and compounding frequency are related but distinct.
• Expect small differences from rounding. An institution may calculate interest at greater precision and round only when posting it.

A result of zero days is zero interest in this formula. The maximum day input is a calculator limit, not a claim about how long any particular account permits interest to accrue.

Frequently Asked Questions

Does accrued interest mean I owe money now?
Not necessarily. It means interest has accumulated. The payment due date and whether the amount is currently payable depend on the account’s terms and billing schedule.

Is accrued interest the same as compound interest?
No. Accrued interest is an amount accumulated over time. Compound interest is interest calculated on principal plus interest already added to the balance. Interest can accrue under either a simple or compounding method.

How do I calculate accrued interest per day?
For simple interest, divide principal multiplied by the annual rate expressed as a decimal by the day-count basis. With $20,000 at 8% and a 365-day basis, the estimate is about $4.38 per day.

Why does my statement differ from this estimate?
The account may use a different day-count convention, a changing balance, compounding, payment-date rules, or more precise calculations before rounding. Check the statement details and the applicable account terms.

Does accrued interest increase my principal balance?
Not automatically. It may be tracked separately, paid on a scheduled date, or added to principal under the account’s terms. This calculator shows a hypothetical principal-plus-interest total but does not establish how an account posts the amount.

This result is an estimate for educational purposes; the lender’s disclosure or account statement gives the exact figures.

Related

• Textura Payment Management System Explained
• U.S. Bank Extra Payment Calculator: Estimate Loan Payoff
• Textura Payment Management Pricing Explained

in p | Principal balance | $ | 20000 | 0 | 100000000
in apr | Annual interest rate | % | 8 | 0.01 | 100
in days | Days accrued | days | 30 | 0 | 36500
in basis | Days in year | days | 365 | 1 | 366
out interest | Accrued interest | $ | p * (apr / 100) * days / basis | 2
out total | Principal plus accrued interest | $ | p + interest | 2