Daily Accrued Interest Calculator and Formula

This daily accrued interest calculator estimates the interest a balance earns or incurs over a specified number of days using a stated annual interest rate. Enter the balance, annual rate, and days; it returns accrued interest and the balance including that interest, before any payment, fee, or rate change.

Formula

The calculator uses simple interest on an actual/365 basis: accrued interest equals the starting balance multiplied by the annual rate as a decimal, multiplied by the number of days, and divided by 365.

• Interest = Balance × (annual rate ÷ 100) × days ÷ 365
• Balance with accrued interest = starting balance + accrued interest

Balance is the amount on which interest accrues, in dollars. Annual rate is entered as a percentage per year, so 8 means 8%, not 0.08. Days is the number of days interest accrues. The result is rounded to the nearest cent for display. This method assumes the balance and rate stay unchanged throughout the interval.

Worked Example

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

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

The unrounded interest calculation is $131.506849…; rounding the displayed interest to cents gives $131.51. A statement or lender calculation can differ by a cent if it carries unrounded daily amounts or applies a different convention.

How Daily Accrual Works

Interest accrues as time passes, even if it is only posted to an account periodically. A daily accrual calculation assigns a portion of the annual interest to each day. Under the simple-interest method shown here, each day’s interest is based on the same starting balance. The daily amount is balance × annual rate ÷ 365, and multiplying that amount by the number of days produces the estimate.

For example, a creditor may calculate interest day by day but add the accumulated amount to a statement balance monthly. Accrual and posting are different events: accrued interest is the amount earned or owed over time, while posting is when it is recorded in the account. Whether posted interest then earns interest depends on the account’s terms and calculation method.

The calculator uses a 365-day denominator throughout the year. Some products instead use a 360-day year, the actual number of days in a year, or another contractual convention. A leap year can matter when the agreement specifies an actual/actual method. Check the relevant statement or account disclosure for the applicable basis; do not assume every product uses this calculator’s convention.

When to Use the Estimate

This calculation can help estimate interest for a fixed balance and rate over a short interval—for example, to understand roughly how much interest could accrue between two dates. It can also help check the scale of a figure shown on a statement. It is not an exact payoff quote: a payoff amount may include transactions, fees, timing rules, or other amounts not represented here.

• Use the balance that actually accrues interest, rather than an unrelated original amount.
• Enter the annual rate as a percentage, such as 8 for 8%.
• Count the days in the interval according to the account’s stated start and end date convention.
• Compare the result with the account’s own disclosed calculation method.

If payments, withdrawals, or rate changes happen during the period, one calculation for the entire interval cannot represent the changing balance accurately. Split the timeline into intervals where the balance and rate are constant, calculate interest for each interval, and add the results. For a payment that reduces principal, use the lower balance for the days after the payment takes effect, subject to the account’s timing rules.

Common Sources of Differences

A frequent mistake is treating an annual percentage as a daily rate. The entered 8 means 8% per year; the formula converts it to 0.08 and prorates it by days. Entering 0.08 instead would mean 0.08%, producing an answer one hundred times smaller.

Another source of mismatch is the day-count denominator. With the defaults, using 360 rather than 365 gives $20,000 × 0.08 × 30 ÷ 360 = $133.33, instead of $131.51. Neither figure should be substituted for an account’s disclosed method without checking its terms. Rounding can also cause small differences: some calculations round each day’s interest before accumulating it; others keep extra decimal places and round only the final amount.

Finally, simple daily accrual is not the same as daily compounding. This calculator does not add each day’s interest to the balance before calculating the next day’s interest. If interest compounds during the period, or is calculated using an average daily balance that changes with transactions, the result may differ.

Assumptions and Limits

• The balance and annual rate remain fixed for the entered number of days.
• Interest is simple, not compounded during the interval.
• The day-count basis is actual days divided by 365, including in leap years.
• The result excludes payments, purchases, withdrawals, fees, penalties, and other adjustments.
• The annual rate entered is the rate applicable to this balance; the calculator does not determine which rate applies.

For a precise account figure, use the method and dates stated by the institution or creditor. The calculator is a general arithmetic estimate, not a substitute for an account statement or disclosure.

Frequently Asked Questions

How do I calculate daily accrued interest?
Multiply the balance by the annual rate written as a decimal, then multiply by the number of days and divide by the applicable day-count denominator. This calculator uses 365.

Is daily accrued interest the same as daily compound interest?
No. Simple daily accrual prorates interest against a fixed balance. Daily compounding adds interest to the balance at intervals so later interest can be calculated on that increased amount.

Why does my statement show a different amount?
The account may use a different day-count basis, a changing daily balance, a different rate, payment timing rules, or a different rounding method. Check the account’s stated calculation method and transaction dates.

Does this calculator include payments or fees?
No. It assumes one unchanged starting balance and excludes payments, fees, and other account activity. For a changing balance, calculate separate intervals using the balance and rate applicable to each one.

Should I use 365 or 360 days?
Use the basis specified for the relevant account. The calculator uses 365 as a general estimate and cannot identify the convention in a particular agreement.

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

Related

• Equity Release Maximum Borrowing Calculator
• Borrowing Power Using Equity: Estimate Your Options
• Calculate Borrowing Power With Equity

in bal | Starting balance | $ | 20000 | 0 | 100000000
in apr | Annual interest rate | % | 8 | 0.01 | 100
in days | Days accrued | days | 30 | 0 | 36500
out int | Accrued interest | $ | bal * apr / 100 * days / 365 | 2
out end | Balance with accrued interest | $ | bal + int | 2