The fastest way to calculate daily accrued interest is the simple formula: Principal × (Annual Rate ÷ Day-Count Basis) × Days Accrued. If you owe $3,000 at 26.99% APR on a 365-day basis, that is $3,000 × (0.2699 ÷ 365) × 1 = $2.22 per day. The trick isn’t the multiplication—it’s knowing which basis your lender uses and how to count the days. Below I’ll walk through the exact worksheet I use after a decade of reconciling loan, bond, and deposit interest for real portfolios.
What the Daily Accrued Interest Formula Actually Looks Like
The general accrued interest formula is Accrued Interest = P × R × (D / B), where P is principal, R is annual rate as a decimal, D is number of days, and B is the day-count basis. The daily variant simply sets D = 1, or you compute the daily rate first: Daily Rate = R / B. This answers the common search ‘what’s the formula for accrued interest?’—it’s the same equation, scaled by time.
Most top results show only P×(r/365)×d. In practice, B is rarely 365 for every product. I’ve seen commercial loans use 360, Treasury bonds use actual/actual, and municipal bonds use 30/360. Using the wrong B over a $500,000 principal can skew accrual by hundreds of dollars per month.
Why the ‘R’ Must Be a Decimal, Not a Percent
A mistake I made early on was plugging 26.99 directly into the formula. You must divide the APR by 100 first. So 26.99% becomes 0.2699. If you forget, your accrued interest is 100× too large—a glaring error that once made a client think their card charged $225 daily instead of $2.25.
APR vs APY: The Rate Input Changes With Compounding
If the product compounds daily, the nominal APR is not the same as the effective daily growth rate. The daily rate is still R/B, but the accrued amount after D days is P×(1+R/B)^D − P. For simple accrual (most loans), it’s linear. For savings and cards, it’s exponential. Knowing which formula applies is step zero before touching the calculator.
The ‘What Is the Formula for Accrued Interest?’ Answer in Plain Terms
Strip away jargon: accrued interest is just the lender’s or depositor’s fair share of annual interest for the exact slice of time money was lent. The formula allocates that slice using days, and the denominator B defines what a ‘year’ means to that contract. Miss the denominator and you misallocate.
A Day-Count Convention Cheat Sheet by Product Type
After auditing portfolios across banks, credit unions, and treasury desks, I compiled this cheat sheet. It’s the missing piece in most ‘how to calculate daily accrued interest’ guides because they treat 365 as universal. It isn’t.
| Product / Instrument | Common Day-Count Basis | Real-World Note |
|---|---|---|
| U.S. Federal Student Loans | Actual/365 | Divisor is 365 even in leap years; servicers do not switch to 366. |
| Credit Cards (U.S.) | Daily Periodic Rate = APR/365 | According to the Consumer Financial Protection Bureau, issuers must disclose the daily rate; some count 366 days in leap years without rate adjustment. |
| Commercial Bank Loans | Actual/360 | Borrower pays 365/360 of stated rate effectively—a hidden ~0.14% premium. |
| Consumer Mortgages (U.S.) | Actual/365 or 30/360 | Check note; 30/360 treats each month as 30 days, ignoring short February. |
| Government Bonds (Treasuries) | Actual/Actual | Uses real days elapsed and real days in year (366 in leap). |
| Corporate & Municipal Bonds | 30/360 (Bond Basis) | Assumes 360-day year, 30-day months; simplifies but biases short months. |
| Savings Accounts / Deposits | Actual/365 or 366 | Compounds daily; leap year adds one extra day of tiny interest. |
Most people don’t realize that a loan quoted at 6% with Actual/360 actually costs 6.083% effective annually versus 6% under Actual/365. That gap is why the cheat sheet matters.
Decoding the Four Bases
30/360: Every month is 30 days, year is 360. Used in corporate bonds. Actual/360: Real days elapsed, but divide by 360—common in bank loans, secretly raises yield. Actual/365: Real days, divide by 365 (or 366 if contract says actual/366). Actual/Actual: Both numerator and denominator use real calendar days; the gold standard for government debt.
Step-by-Step Worksheet: From Rate to Accrued Dollars
Here is the four-step worksheet I hand new analysts. It converts any loan or deposit into a daily accrual number without guesswork.
Step 1: Find the Rate and Basis
Locate the APR or coupon rate in the note. Identify the day-count basis from the cheat sheet or contract. If the contract is silent, assume Actual/365 for consumer loans, but confirm with the lender. Write both values at the top of your sheet.
Step 2: Compute the Daily Rate
Divide the decimal rate by the basis: Daily Rate = R / B. Example: 26.99% APR, B=365 → 0.2699/365 = 0.00073945. For a $10,000 loan at 5% on Actual/360, daily rate = 0.05/360 = 0.00013889.
Step 3: Count the Days
Count days from the last payment or settlement date up to but not including the current date (or including, per convention). We’ll detail this in the next section. Leap years and month-ends trip up most manual counts. Mark the start and end dates explicitly.
Step 4: Multiply
Daily Accrued = Principal × Daily Rate. Period Accrued = Daily Accrued × Days. That’s it. If you’d rather skip the spreadsheet, our Daily Interest Calculator applies these conventions automatically.
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Downloadable template: copy the table columns (Principal, Rate, Basis, Days, Accrued) into Google Sheets. Use the formula =A2*(B2/C2)*D2. That’s a ready-to-use daily accrual template. For compounding, use =A2*(1+B2/C2)^D2-A2.
Side-by-Side: $3,000 at 26.99% APR Under 360 vs 365
The search ‘how much is 26.99 APR on $3000?’ deserves a precise, basis-aware answer. Below is the exact math I ran when a friend questioned her credit card statement.
Calculation with 365-Day Basis
Daily Rate = 0.2699 / 365 = 0.000739452. Daily Interest = $3,000 × 0.000739452 = $2.21836 (about $2.22). Over a 30-day cycle: $66.55. Over 365 days: $809.70 (the quoted APR exactly).
Calculation with 360-Day Basis
Daily Rate = 0.2699 / 360 = 0.000749722. Daily Interest = $3,000 × 0.000749722 = $2.24917 (about $2.25). Over 30 days: $67.48. Over 365 days (real days): $820.95—an extra $11.25 because the divisor is smaller but days are real.
The difference between 360 and 365 on a modest $3,000 balance is roughly $0.03 per day. Scale that to a $30,000 balance and you’re talking $3.00/day or $1,095/year in hidden basis cost.
This side-by-side is why the formula for daily accrued interest must specify B. The same APR produces different real dollars. The effective APR under 360 basis is 0.2699 × (365/360) = 27.36%, not 26.99%.
Counting Days Correctly (Including Leap Years and Payment Timing)
When I first tried to reconcile accrued interest on a municipal bond settlement in February 2020—a leap year—I used a flat 365-day divisor and counted 29 days for February. I was off by $37.22 on a $500k principal versus the back office. The error wasn’t the rate; it was ignoring Actual/Actual.
The ‘Include/Exclude’ Rule
Most loan accruals use the actual/actual or actual/365 convention where you count days from the last payment date excluding that date and including the accrual end date (or vice versa per contract). A standard practice: if payment posted on the 1st, day 1 is the 2nd. Missing this shifts accrual by one day—small on $3k, large on $3M.
Concrete Date Example
Suppose last payment was March 15, and you accrue through April 14. Excluding March 15, days left in March = 16 (16th–31st). Plus 14 days in April = 30 days. If you accidentally include the 15th, you get 31 and overstate by 3.3% on a 30-day bill.
Leap-Year Handling
Under Actual/365, February 29 is ignored (year still 365). Under Actual/366 or Actual/Actual, it counts and the divisor becomes 366. Credit cards often keep the 365 divisor but charge for 366 days, effectively an extra day’s interest. Always read the cardholder agreement.
Month-End Shortcuts
For 30/360, February 28 (or 29) is treated as 30 days. If you manually count, you must roll 28 to 30. I’ve seen junior accountants accrue only 28 days, understating bond interest by 2 days—a fix that required a correcting journal entry.
Simple vs Compounding Daily Accrual — and Where Each Shows Up
Simple daily accrual means interest does not earn interest: Accrued = P × (R/B) × D. Compounding daily means each day’s interest attaches to principal for the next day: Accrued = P × (1 + R/B)^D − P.
Student loans and most mortgages use simple accrual—interest is calculated on the stated principal balance, not on prior unpaid interest (unless capitalized). Credit cards and savings accounts compound. The CFPB notes card issuers apply daily compounding if you carry a balance, which makes the effective cost higher than the nominal APR.
When Compounding Bites
On $3,000 at 26.99% with daily compounding over 30 days, you owe $66.98 vs $66.55 simple—a $0.43 difference. Over a year, compounding adds about $12. That’s why the formula for accrued interest must state whether it’s simple or compound.
Deriving the Compound Formula
Start with day 1: P(1+r). Day 2: P(1+r)^2. After D days: P(1+r)^D. Subtract principal to get pure interest. The ‘r’ there is the daily rate R/B. This is standard in deposit accounting and card finance.
Beyond Student Loans: Mortgages, Bonds, and Savings Examples
Competitor articles fixate on student loans. Here are three other real cases that show the framework’s range.
Mortgage Example (Actual/360)
$200,000 at 4.0% on Actual/360. Daily Rate = 0.04/360 = 0.00011111. Daily Interest = $22.22. Over 30 days = $666.67. Had it been Actual/365, daily would be $21.92, saving $9/month. On a 30-year loan that basis choice adds thousands.
Corporate Bond Example (30/360)
$1,000,000 face, 5% coupon, 30/360. Accrued for 60 days since coupon: $1,000,000 × 0.05 × (60/360) = $8,333.33. If you mistakenly used actual 58 days (Feb-Mar), you’d underpay by $277.
Savings Account Example (Actual/366)
$10,000 at 3% APY compounding daily in leap year. Daily Rate = 0.03/366 = 0.00008197. Day 1 interest = $0.82, which then earns interest day 2. Over the year you get $304.05 vs $300 flat—small but real.
Treasury Bill Example (Actual/Actual)
A $100,000 T-bill at 2.5% for 90 actual days in a 366-day leap year: Accrued = 100,000 × 0.025 × (90/366) = $614.75. Using 365 would give $616.44—a $1.69 slip that fails government reconciliation.
Common Mistakes I’ve Made and Seen Others Make
The thing nobody tells you about accrual work is that the math is easy; the data is hard. Here are field-tested traps.
- Using 365 when the contract says 360—adds 1.4% effective cost.
- Counting the payment day twice (both as end of old period and start of new).
- Forgetting to convert APR to decimal; result off by 100×.
- Ignoring leap years in Actual/Actual bonds—my February 2020 error.
- Assuming credit card daily rate changes in leap year; many don’t.
- Applying simple formula to compounding product, understating true interest.
- Trusting a calculator that hides the basis; always ask what B it uses.
When in doubt, reconcile to the lender’s posted accrual for one day. If your number differs by more than a cent per $10k, recheck basis and day count.
Authoritative accrual calculation is 80% convention mapping and 20% arithmetic. Master the Day-Count Convention Cheat Sheet and you’ll outperform most finance grads on day one.
For legal judgments or statutory interest, the basis may be set by court rule; our Default Judgment Interest Calculator handles those niche day counts if you encounter them.