A daily interest calculator handles the periods that annual formulas cannot: 45 days on an overdraft, 17 days between a drawdown and a repayment, the stub period at the start of a loan before the first full month begins. Interest on most credit accrues daily whether or not it is charged monthly, and over a partial period the day-count convention in the agreement determines the amount.
Arb Digital publishes this in the free tool library at arbsbuy.com with all three conventions side by side, because that comparison is the part most calculators leave out. It differs from the live simple interest calculator, which works in whole years and has no concept of a day-count basis at all — a distinction that stops mattering only when the period happens to be an exact number of years.
What This Daily Interest Calculator Does
Enter a principal, an annual rate and a number of days, and the tool derives the daily periodic rate on your chosen basis and applies it. It then computes the same period on the other two bases, so the cost of the convention is visible rather than assumed, and it reports the daily-compounded figure alongside the simple one.
The daily periodic rate in the grid is the number your statement is really using. Most lenders do not charge an annual rate; they charge a daily rate derived from it, and the derivation is the convention. The Consumer Financial Protection Bureau describes this directly in its explanation of what a daily periodic rate is on a credit card, noting that the rate is generally found by dividing the annual percentage rate by either 360 or 365, depending on the issuer.
The third grid item prices that choice. It is the difference between the 360-basis and 365-basis charge for your figures — small on a short period and a modest balance, and not small at all on a large facility carried across a year.
How to Use It
- Find the basis in the agreement before assuming one. Commercial loans and many overdrafts use a 360-day year; consumer credit more often uses 365.
- Count days the way the contract counts them. The usual convention includes one end date and excludes the other, so a loan drawn on the 1st and repaid on the 16th accrues fifteen days, not sixteen.
- Enter the nominal annual rate. If you enter an effective annual rate that already includes compounding, and then select daily compounding, you will count it twice.
- Use the balance that was actually outstanding. On a facility that moved during the period, run each balance for its own number of days and add the results.
- Compare all three bars before accepting a lender's figure. If the amount charged does not match any of them, the difference is worth asking about.
The Formula / How It's Calculated
Simple daily interest is principal × (annual rate ÷ days in the year) × number of days, where the days in the year is 360, 365 or 366 depending on the convention. Daily compounding instead uses principal × ((1 + annual rate ÷ days in the year) raised to the power of the number of days, minus one).
Run the defaults. A principal of 25,000 at 7.50 percent produces 1,875 of interest in a full year. On an actual/365 basis the daily periodic rate is 0.075 ÷ 365 = 0.00020548, so daily interest is 25,000 × 0.00020548 = 5.14, and 45 days costs 231.16.
Change only the convention. On a 360-day basis the daily rate is 0.075 ÷ 360 = 0.00020833, daily interest is 5.21, and the same 45 days costs 234.38 — an extra 3.21 for an identical rate over an identical period. On a leap-year 366-day basis it costs 230.53. With daily compounding on the 365 basis the figure rises to 232.21, because each day's interest joins the balance the following day. The balance including simple interest is 25,000 + 231.16 = 25,231.16.
Why a 360-Day Year Costs More
The 360-day convention looks like a simplification and functions as a price increase, and the reason is worth setting out because it surprises people every time.
Dividing the annual rate by 360 rather than 365 makes each individual day more expensive by a factor of 365 ÷ 360, or about 1.39 percent. But the lender then charges for the actual number of days elapsed, which over a full year is 365 — not 360. The result is that a rate quoted as 7.50 percent on an actual/360 basis actually costs 7.50 × 365 ÷ 360 = 7.604 percent over a calendar year. The convention adds roughly 10 basis points to a 7.50 percent rate, and proportionally more to a higher one.
The convention has a genuine historical origin in the era before computers, when a 360-day year of twelve thirty-day months made manual interest tables tractable. It survives mainly because it is embedded in commercial loan documentation. The practical response is simply to convert before comparing: multiply a 360-basis rate by 365 ÷ 360 to get the equivalent 365-basis rate, then compare like with like. In the units of the basis point calculator, the difference is real and quotable, and on a large facility it is worth negotiating.
Counting the Days Correctly
The day count is where most disputes about a small interest figure actually originate, and the rules are conventional rather than obvious.
The standard treatment includes the first day and excludes the last, or the reverse — either is defensible, but the agreement picks one. Borrow on the 10th and repay on the 25th and you owe fifteen days of interest, not sixteen. Over a single period the difference of one day is trivial; on a revolving facility drawn and repaid weekly, a systematic one-day error repeated fifty times a year is not.
Month ends complicate it further. A loan drawn on 31 January with a monthly interest date has no 31 February to fall on, and agreements handle this with a business-day or end-of-month rule that shifts the date and therefore the day count. Weekends and public holidays matter too: interest normally accrues on non-business days even though payments cannot settle on them, so a repayment made on a Friday for value the following Monday accrues three extra days. Because the day count is entered directly on this page, the tool computes whatever period you give it — getting the count right from the agreement is the part it cannot do for you.
Where Daily Accrual Actually Bites
Daily accrual has one consequence that matters more than the arithmetic: on an account without a grace period, paying earlier costs less, and paying part of a balance early costs less in proportion.
This is the mechanism behind the CFPB's explanation of how a credit card company calculates the interest owed, which sets out that many issuers compute interest daily against the average daily balance. Where that is the method and no grace period applies, a payment made on the 3rd rather than the 20th removes seventeen days of accrual on that amount — a saving available for nothing more than timing. The credit card interest calculator models a revolving balance over months; this page is the underlying daily mechanic.
The same logic runs through business borrowing. On a revolving facility, sweeping surplus cash into the account for a few days between collections and payments reduces the balance interest accrues on, which is one of the few genuinely free improvements available to a business with a facility and a lumpy cash cycle. Whether it is worth the administrative effort is a question of scale, and the numbers here answer it directly: a hundred thousand parked for ten days at 7.50 percent on a 365 basis saves 205.48. Published benchmark rate series such as the Federal Reserve's H.15 selected interest rates release are quoted as annual percentages, so any of them can be dropped into the rate field here to see what a day of it is worth.
Simple Versus Daily Compounding
The compounding selector changes the arithmetic in a way that is negligible over days and substantial over years, and knowing where the crossover sits stops both over- and under-estimating it.
On the defaults the gap is 232.21 against 231.16 — about one currency unit over 45 days, or four tenths of a percent of the interest. Extend the same balance and rate to 365 days and simple interest is 1,875 while daily compounding produces 1,946.90, a difference of 71.90. The gap grows with the rate and with the length of the period, and it grows fastest on unpaid balances at high rates, which is why revolving consumer credit is where daily compounding is most visible.
The distinction that matters in practice is whether unpaid interest is capitalised — added to the principal so that it subsequently earns interest itself. Many term loans do not capitalise: interest is charged and paid monthly, so it never joins the principal, and simple daily accrual describes the position correctly. Revolving accounts and arrears situations often do capitalise. If you are unsure which applies, the agreement's treatment of unpaid interest is the clause to read, and the compound interest calculator shows what the difference becomes over multiple years.
Arb Digital keeps a large library of free finance and marketing tools at arbsbuy.com, all of them ad-supported and none of them behind a signup.
Browse the Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Assuming a 365-day basis — commercial loans and many overdrafts use 360, which quietly raises the effective rate by around 1.4 percent of itself.
- Counting both end dates — the usual convention includes one and excludes the other, so a 10th-to-25th period is fifteen days.
- Entering an effective rate then selecting compounding — the compounding is then applied twice and the result is overstated.
- Using the opening balance for a period when it changed — split the period at each movement and run each balance for its own days.
- Ignoring weekends and holidays — interest normally accrues on non-business days even though settlement cannot happen on them.
Related Free Tools From Arb Digital
Pair this with the simple interest calculator for whole-year periods, the compound interest calculator for what daily accrual becomes over years, the credit card interest calculator for a revolving balance, the APR calculator when fees are wrapped into the quoted rate, the loan payoff calculator for the effect of paying early, and the basis point calculator for what the convention difference is worth in bps. The full free online tools hub lists everything else.
Frequently Asked Questions
Divide the annual rate by the number of days in the year used by your agreement, multiply by the principal to get the daily amount, and multiply that by the number of days. At 7.50 percent on 25,000 with a 365-day basis, one day is 5.14.
It is the annual rate divided by the days in the year, and it is the rate a lender actually applies each day. Issuers commonly divide the annual percentage rate by either 360 or 365 to reach it.
It is a convention that predates computers, when a year of twelve thirty-day months made manual interest tables workable. Because interest is still charged for the actual days elapsed, it raises the effective cost by roughly 1.4 percent of the quoted rate.
The 360-day basis, for any given quoted rate. Dividing by a smaller number makes each day more expensive while the lender still charges for all 365 days of a calendar year.
The way the agreement does, which is normally to include one end date and exclude the other. A balance drawn on the 10th and repaid on the 25th accrues fifteen days of interest rather than sixteen.
On most credit it does. Payments cannot settle on non-business days, but accrual continues, so a payment made on a Friday for value the following Monday carries three extra days of interest.
Simple interest is calculated on the original principal throughout. Daily compounding adds each day's interest to the balance so it earns interest itself. Over 45 days the gap is about one unit on these figures; over a full year it is far larger.
On an account that accrues daily without a grace period, yes, in direct proportion to the days removed. Paying 100,000 ten days earlier at 7.50 percent on a 365 basis saves 205.48.
This calculator performs arithmetic on figures you supply and is provided for general information only. It is not financial, lending or tax advice, and day-count conventions and compounding treatment differ between agreements and jurisdictions — confirm any figure against your own credit agreement or with a qualified professional.
