Accrued Interest: How It Builds on Loans and Savings

Accrued interest is interest that has built up over time but has not yet been paid or received. This calculator estimates simple accrued interest from a principal balance, annual interest rate, and elapsed time, so you can see the amount accumulated over that period.

Formula

This calculator uses a simple-interest, actual/365 estimate: accrued interest equals principal multiplied by the annual rate, expressed as a decimal, multiplied by the fraction of a year elapsed.

I = P × (APR / 100) × (d / 365)

• I is accrued interest, in dollars.
• P is the principal balance, in dollars.
• APR is the annual interest rate, entered as a percentage.
• d is the number of elapsed days.

The second result is P + I, the principal plus the estimated accrued interest. The formula assumes the principal stays unchanged and does not compound interest during the period. Actual financial products may use a different day-count convention, compounding schedule, or balance calculation.

Worked Example

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

1. Convert the annual rate to decimal form: 8 / 100 = 0.08.
2. Express elapsed time as a fraction of a 365-day year: 30 / 365 ≈ 0.08219178.
3. Multiply: $20,000 × 0.08 × (30 / 365) = $131.5068, which rounds to $131.51 accrued interest.
4. Add interest to principal: $20,000 + $131.51 = $20,131.51.

What Accrued Interest Means

Interest is generally the price paid for using borrowed money or the return earned for allowing money to be used or deposited. It accrues as time passes according to the account’s terms. “Accrued” describes when the interest has been earned or incurred, not necessarily when cash changes hands.

For a borrower, interest can accrue between payment dates. For a saver or investor, interest may accrue before it is credited or paid. A statement might therefore show interest accumulated during a period even if the scheduled payment or credit occurs later. Whether accrued interest is already included in a displayed balance depends on how the institution presents that balance.

How Accrual and Compounding Differ

Accrual tracks interest over time. Compounding determines whether previously accrued interest is added to the balance used to calculate later interest. With simple interest, interest is calculated on the original principal. With compounding, interest may be calculated on principal plus interest already added to the account.

For example, at a constant 8% annual simple rate on $20,000, a 30-day period using actual/365 produces about $131.51. A real account may calculate interest daily, add it to the balance on a schedule, and then accrue later interest on that larger balance. The result can differ, even if the advertised annual rate looks similar.

Accrued interest is also not automatically the same as a required payment, a late fee, or the total cost of borrowing. Those amounts depend on the contract and payment history. This estimate models only interest on a fixed principal for the entered number of days.

When This Estimate Is Useful

A simple estimate can help explain why a balance changes between payment dates or provide a rough check on interest for a short, unchanged-balance period. It can also illustrate how principal, annual rate, and time affect interest: holding two inputs constant, increasing the third increases the estimate.

• Use the principal that actually bears interest, not necessarily the original amount borrowed.
• Enter the annual rate as a percentage, such as 8 for 8%, rather than 0.08.
• Count the elapsed days relevant to the period you want to estimate.
• Compare the result with the account statement or contract, which defines the institution’s calculation method.

For a loan with changing balances, such as one with regular payments, interest should be calculated on each applicable balance over its own time interval. A fixed-principal estimate will not reproduce an amortization schedule. For an investment or deposit, credits, withdrawals, tiered rates, and account-specific rules may also affect the amount.

Common Sources of Differences

A calculator result may not match a statement because financial products do not all count days or apply interest in the same way. Some calculations use a 365-day year; others may use a different denominator or a prescribed monthly period. Leap-year handling, the exact start and end dates, whether a day is included, and rounding at each step can also matter.

• Changing principal: Payments, deposits, withdrawals, or charges change the amount on which interest accrues.
• Compounding: Adding interest to principal can make subsequent interest larger.
• Rate changes: If the rate changes during the period, calculate each segment using its applicable rate and duration.
• Rounding: Institutions may round daily interest or statement totals differently from a calculator that rounds only the final result.
• Fees and other charges: These are not interest and are not included here, though account terms may treat certain amounts as part of an interest-bearing balance.

For an exact figure, check the agreement or statement for the annual rate, day-count basis, compounding method, balance used, and dates. This calculator is a transparent illustration, not a substitute for those details.

Frequently Asked Questions

Is accrued interest already included in my balance?
It depends on how the balance is defined and displayed. Some balances include interest through a particular date; others show accrued interest separately. Check the statement’s labels and the account terms.

Does accrued interest mean interest has been paid?
No. It means interest has accumulated or been earned over time. Payment or credit may happen later, depending on the product’s schedule and terms.

Does accrued interest earn interest?
Not necessarily. It earns additional interest when the applicable terms compound it by adding it to the interest-bearing balance. Under simple interest, the calculation remains based on the original principal.

Why does my lender’s amount differ from this calculator?
This estimate assumes a fixed principal, a constant rate, simple interest, and an actual/365 day basis. The lender may use daily compounding, another day-count convention, a changing balance, or different rounding.

Can accrued interest be negative?
Interest can be reversed or adjusted in some account records, but this calculator estimates interest accumulation for a nonnegative principal and rate. It does not model reversals, credits, or corrections.

This result is an estimate for education, and the lender’s disclosure or account statement gives the applicable figures and calculation method.

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in p | Principal balance | $ | 20000 | 0 | 100000000
in apr | Annual interest rate | % | 8 | 0 | 100
in days | Days accrued | days | 30 | 0 | 36500
out int | Accrued interest | $ | p * apr / 100 * days / 365 | 2
out total | Balance including accrued interest | $ | p + int | 2