Accrued Interest: How It Builds on Loans and Savings

Accrued interest is interest that has accumulated over time but has not yet been paid or credited. This calculator estimates simple interest for a chosen principal, annual rate, and number of days, so you can see how much has built up between payment or posting dates.

Formula

For this estimate, accrued interest equals principal multiplied by the annual rate and the fraction of a 365-day year that has passed:

I = P × (APR ÷ 100) × (d ÷ 365)

• I is accrued interest, in dollars.
• P is the principal or balance on which interest accrues, in dollars.
• APR is the annual interest rate entered as a percentage.
• d is the number of days in the accrual period.

The second calculator result is P + I, the principal plus the estimated accrued interest, assuming no intervening payments, deposits, fees, or changes in balance. The calculation uses a simple-interest, 365-day convention. Actual financial products can define accrual and day-count conventions differently.

Worked Example

Using the calculator’s defaults—$20,000 principal, an 8% annual rate, and 30 days:

1. Convert the percentage to a decimal: 8 ÷ 100 = 0.08.
2. Find the annual interest on the principal: $20,000 × 0.08 = $1,600.
3. Find the fraction of the year: 30 ÷ 365 ≈ 0.0821918.
4. Multiply: $1,600 × 30 ÷ 365 ≈ $131.5068.

Rounded to cents, estimated accrued interest is $131.51. Principal plus that interest is $20,131.51. These results use the displayed formula; a lender or savings provider may use a different day-count basis, compounding schedule, or balance calculation.

How Accrued Interest Works

Interest is compensation for the use of money, calculated according to an agreement or account terms. Accrual describes when the interest is earned or incurred; payment describes when money is actually transferred. Those events are often separated. A borrower can owe interest that has accumulated since the last payment, while a saver can earn interest that has accumulated since the last credit to the account.

With simple interest and an unchanged balance, interest grows in proportion to both time and principal. If the balance or rate changes, calculate each period separately using the relevant balance, rate, and number of days, then add the amounts. If unpaid interest is added to principal, later interest may be calculated on that larger balance; this is compounding, not the simple-interest estimate shown here.

For example, $20,000 at 8% accrues about $4.38 per day under a 365-day simple-interest convention: $20,000 × 0.08 ÷ 365. Thirty days therefore produces about $131.51. The daily amount is an estimate, not necessarily the exact amount on a statement, because account terms may use a different convention or changing daily balances.

Where You Encounter It

• Loans: Interest can accrue between payment dates. A payment may cover accrued interest first, with the remainder reducing principal, depending on the loan’s terms and payment allocation.
• Savings and deposit accounts: Interest can accumulate during a period and be credited later. The credited amount may then contribute to future interest if the account compounds.
• Bonds and other investments: Interest may build between scheduled payment dates. In some transactions, accrued interest is accounted for separately from the quoted price. The instrument’s terms determine the calculation.
• Accounting: Records may recognize interest as it is earned or incurred even before cash is received or paid. Accrued interest is not necessarily the same as interest already posted to an account.

What Changes the Amount

Before relying on a calculation, identify the balance that earns interest, the applicable rate, the exact period, and the product’s calculation rules. Useful details to check in an account statement or agreement include:

• Whether the rate is fixed or variable, and when a variable rate can change.
• Whether interest uses a 360-day, 365-day, or another day-count basis, and how the start and end dates are treated.
• Whether interest accrues on a daily balance, average balance, or another defined amount.
• How often interest compounds or is credited, and whether unpaid interest is added to the balance.
• Whether payments, deposits, withdrawals, or other balance changes occurred during the period.

A 360-day convention can produce a different result from a 365-day convention for the same nominal annual rate and days. Likewise, a variable balance cannot be represented accurately by applying one starting principal to the entire period. Use the actual statement or contract method when an exact figure matters.

Common Misunderstandings and Limits

Accrued does not mean paid. Interest can be accumulating without appearing as a separate cash transaction yet. Conversely, a displayed or posted amount may reflect a completed crediting process rather than all interest currently building up.

APR is not always the rate used directly for daily accrual. This calculator treats the entered annual percentage as a nominal annual rate and divides the year into 365 days. Some products specify a periodic rate or a different calculation method. Follow the product’s stated terms rather than assuming every APR converts to a daily rate in the same way.

The estimate is not a payoff quote. A payoff amount can involve a current balance, interest through a specific date, payment timing, and contract-specific items. This calculator excludes fees, penalties, taxes, deposits, withdrawals, and payments. It also does not model daily compounding or changing rates. For an exact amount due or credited, consult the account provider’s statement or disclosure.

Frequently Asked Questions

Is accrued interest the same as interest paid?
No. Accrued interest has built up, but it may not have been paid by a borrower or credited to a saver yet. Whether it is due, posted, or added to a balance depends on the product’s schedule and terms.

How do I calculate accrued interest per day?
For simple interest using a 365-day year, divide principal multiplied by the annual rate as a decimal by 365. On $20,000 at 8%, that is $20,000 × 0.08 ÷ 365, or about $4.38 per day.

Does accrued interest earn interest?
It can if the account or loan compounds by adding accrued interest to the balance used for later calculations. Under simple interest, interest is calculated on the original principal instead. The terms determine which method applies.

Why does my statement differ from this estimate?
The statement may use a different day-count basis, exact dates, changing daily balances, compounding, payment timing, or a rate that changed during the period. This calculator assumes one rate, one principal, and a 365-day simple-interest method.

Can accrued interest be negative?
Interest accrued under a positive rate on a positive balance is not negative in this model. A negative rate or a balance treated as a debt rather than principal would require interpreting the account terms and calculation differently.

This result is an estimate for education; the lender’s or account provider’s disclosure gives the exact figures.

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in p | Principal amount | $ | 20000 | 0 | 100000000
in apr | Annual interest rate (APR) | % | 8 | 0.01 | 100
in days | Days accrued | days | 30 | 0 | 36500
out ai | Accrued interest | $ | p * (apr / 100) * days / 365 | 2
out bal | Principal plus accrued interest | $ | p + ai | 2