Simple Interest Calculator
Simple interest is I = P x R x T and takes four seconds to work out, so the fair question is why it needs a page. The answer is the T. A term counted in days has to be divided by an assumed year length, and US commercial lending routinely assumes 360 days instead of 365. That turns a 9.00% note into a 9.125% one without touching the rate on the paper. This calculator makes the day count an input, shows the rate the convention actually charges, and runs the result through Regulation DD's APY formula so you can hold a short-dated deal up against anything else.
The deal
The amount borrowed, lent or deposited.
The term
Actual/360 is standard in US commercial lending and charges 365 days of a rate set for a 360 day year.
Interest
$1,109.59
On $25,000.00 at 9.00% for 180 days.
Compare it to anything else
This is an Actual/365 basis, so the effective rate equals the quoted rate. If your note says interest accrues on a 360 day year, switch the basis: the same rate then costs 1.39% more.
Interest never joins the principal, so nothing compounds and the daily accrual is flat. If your agreement capitalises unpaid interest at any point, use the compound interest calculator instead. No tax, fees, origination charges or prepayment terms are modelled.
Worked example
A $25,000 short-term note at 9% a year, running 180 days, with interest computed on an Actual/365 basis and paid at maturity along with the principal. You want the interest, the daily accrual, and a figure that lets you set this deal beside a compounding one.
Interest is 25,000 x 0.09 x (180/365) = $1,109.59, so $26,109.59 is due at maturity and the note accrues $6.16 a day. The annual percentage yield on those dollars, by Regulation DD's formula 100[(1 + 1,109.59/25,000)^(365/180) - 1], is 9.2054%: above the stated 9% because the formula assumes the money comes back and is re-earned for the rest of the year. Now change one thing and nothing else. Switch the day count to Actual/360 and the same 180 days costs $1,125.00, or $15.41 more, because 180/360 is half a year while 180/365 is not. The effective rate is 9.125%, not 9%. Over a full 365 days the gap opens to the whole difference between the two conventions: $2,250.00 against $2,281.25 on $25,000, and $1,250 a year on a $1,000,000 balance.
The formula is one line. The time fraction is the problem
Simple interest is I = P x R x T. Principal times annual rate times time in years. Interest never joins the principal, so the balance earning interest on the last day is the same as on the first, and the accrual per day is constant.
Everything interesting sits in T, and T is a division. A term in years or months is unambiguous, because six months is half a year to anyone. A term in days is not, because the denominator is a convention rather than a fact. Divide 180 days by 365 and you get 0.4931 of a year. Divide it by 360 and you get 0.5000. On $25,000 at 9% that is the difference between $1,109.59 and $1,125.00.
This calculator makes the denominator an input instead of a hidden assumption, and it only offers the choice when the term is counted in days, because that is the only time the choice exists. A six month term is half a year under either convention and no day count changes it.
One more thing about simple interest: the daily accrual never moves. On the worked example it is $6.16 a day from day one to day 180. If a lender quotes you a per diem that rises over the term, you are not looking at simple interest, whatever the paperwork calls it.
Actual/360 is a rate increase that never appears in the rate
The convention is straightforward once stated. Interest accrues at the annual rate divided by 360, and is charged for the actual number of days elapsed. Since a year has 365 days, a borrower pays 365 days of a rate calibrated to a 360 day year.
The multiplier is 365/360, or 1.0139. A 9.00% note accrues at 9.125%. An 8.00% note accrues at 8.111%. The quoted rate is unchanged, the document is accurate, and the borrower pays 1.39% more interest than the rate implies. On $100,000 at 8% for a year that is $8,111.11 rather than $8,000.00. On $1,000,000 at 9%, it adds $1,250 a year.
None of this is a trick. It is a stated convention and it is normal in US commercial lending. It only becomes a problem when a borrower sets an Actual/360 quote against an Actual/365 quote as though the two rates were the same unit. They are not. Convert both to the same basis first, which is what the effective rate output here is for.
The direction never reverses, which makes it easy to remember. Actual/360 always favours the lender on a loan and always favours the depositor on a deposit, for the same reason: it counts more days of accrual than a 360 day year contains. If you are the one paying, ask which basis the note uses before you compare anything.
When the compounding gap is a rounding error, and when it is not
Simple interest usually gets presented as the poor relation. Over the terms it is actually used for, the difference barely exists, and the numbers below show that rather than assert it.
Take $25,000 at 9%. Over 30 days, simple interest earns $184.93 and monthly compounding earns $184.92: identical, and marginally in simple interest's favour, because a 30 day term does not contain a full compounding period. Over 90 days the gap is $4.09. Over 180 days, $20.66. Over a full year, $95.17 on $2,250 of interest, a bit over 4%. Over three years it reaches $966.13, and by then the choice of convention is real money.
Under a year, then, simple against compound is a rounding error, and arguing about it costs more than it saves. Past a year it compounds, in both senses, and the gap grows faster than the term does.
The same arithmetic explains why short-dated instruments get quoted simple in the first place. There is nothing meaningful to hide over 30 or 90 days, and simple interest is easier to compute, easier to check and easier to prorate if the borrower repays early.
APY is how you compare a simple-interest deal to anything else
A simple-interest quote and a compounding quote are not directly comparable, and the fix is the one US law already mandates for deposits. Appendix A to 12 CFR Part 1030, Regulation DD under the Truth in Savings Act, defines APY = 100 [(1 + Interest/Principal)^(365/Days in term) - 1], where Days in term is the actual number of days in the term.
This page runs your result through that formula. On the worked example the 9% note over 180 days returns an APY of 9.2054%, higher than the stated rate because annualising assumes the money comes back and is re-earned for the rest of the year. The direction reverses past a year: the same 9% simple over three years is an APY of 8.2932%, because a deal that never compounds falls further behind the annualised standard the longer it runs.
You can check the formula against the regulation's own example. Regulation DD states that an institution paying $30.37 in interest on a $1,000 six month certificate, where the six month period contains 182 days, discloses an annual percentage yield of 6.18%. Enter $1,000, 6.0907%, 182 days on an Actual/365 basis, and this calculator returns $30.37 of interest and an APY of 6.1837%. That is the regulation's own figure to two decimal places.
One caution on the exponent. The Reg DD formula uses actual days in the term, so it always divides by 365, even when the interest itself accrued on a 360 day basis. That is deliberate. The accrual convention decides how many dollars you earned, and the APY formula then annualises those dollars over real time. Mixing 360 into the exponent counts the convention twice.
Where merchants meet simple interest, and where they only think they do
Three things on this site run into this page. Start with the one that catches people out.
A merchant cash advance is priced with a factor rate, a flat multiplier with no time in it, so there is no interest rate to put into this calculator and no term to divide by. A 1.30 factor on $50,000 means you repay $65,000 whether it takes six months or eighteen, and the same $15,000 charge is roughly 111% APR at one speed and roughly 37% at another. Type a factor rate in here and the answer is arithmetically fine and financially meaningless. Use the factor rate to APR converter, which solves for the rate that makes the cash you actually received equal the stream of daily payments.
The case that does fit is money held still for a known number of days, and a rolling reserve is the clearest one. A processor holding 10% of your card volume for 180 days is holding a fixed sum for a fixed term, which is exactly the shape this formula wants. At the FDIC money market national average of 0.63%, a $50,000 reserve held 180 days gives up $155.34 of interest. Work that out once and you can see what a reserve does not cost you. The damage is the cash being unavailable to run the business, and calling $155.34 the damage understates it by an order of magnitude.
The third is a short-term note or a working capital line, which is where the day count section earns its place. If you are borrowing against receivables or taking a bank line to bridge a payout cycle, the quote will usually be simple interest on an Actual/360 basis, and the rate you compare it against needs converting before you compare it.
This is arithmetic on the figures you entered, not financial advice and not an offer. Your account agreement or loan note is the authority on what you will actually earn or owe.
$25,000 at 9% across a range of terms, computed on this page rather than sourced. Interest and APY are on an Actual/365 basis. The last column is what the same principal and term would produce with monthly compounding, to show where the gap stops being a rounding error. Every cell is arithmetic you can reproduce with the widget above.
| Fee | Simple interest | Total at maturity | APY | Gap vs monthly compounding |
|---|---|---|---|---|
| 30 daysCompounding is marginally behind here, because a 30 day term does not contain a full monthly compounding period. | $184.93 | $25,184.93 | 9.3812% | -$0.01 |
| 90 days | $554.79 | $25,554.79 | 9.3098% | $4.09 |
| 180 days | $1,109.59 | $26,109.59 | 9.2054% | $20.66 |
| 365 daysAt exactly one year the APY equals the stated rate. It is the only term where the two agree. | $2,250.00 | $27,250.00 | 9.0000% | $95.17 |
| 3 yearsPast a year the APY falls below the stated rate, because a deal that never compounds loses ground against the annualised standard every year it runs. | $6,750.00 | $31,750.00 | 8.2932% | $966.13 |
Assumptions and limits
- Simple interest means interest is never added to the principal, so the accrual per day is constant for the whole term. If your agreement capitalises unpaid interest at any point, even once, this is the wrong calculator and the compound interest calculator is the right one.
- A term entered in days is divided by the day basis you select, 365 or 360. A term entered in months or years is not, because no days were counted: six months is half a year under either convention. The day basis selector therefore only appears when the unit is days, which is the only place it legitimately applies.
- The Actual/360 option models the convention as it is normally written: accrue at the annual rate divided by 360, for the actual number of days elapsed. That produces an effective rate of 365/360 times the quoted rate, so the page reports it separately and the comparison against an Actual/365 quote stays out in the open.
- The APY output uses the general formula in Appendix A to 12 CFR Part 1030 and always divides by the actual days in the term, never by 360, even when the interest accrued on a 360 day basis. That is deliberate. The accrual convention decides how many dollars were earned; the APY formula then annualises those dollars over real elapsed time.
- Months are converted at 365/12 days for the per-day and APY figures. Institutions vary here and some use a 30 day month, so a result stated in months can differ by a few cents from a statement computed another way. Enter the term in days if you need to match a specific document to the cent.
- Nothing here models tax, fees, origination charges, prepayment penalties or early repayment, and it makes no assumption about how the interest is paid. It computes what accrues over the term you entered. Your note or account agreement governs everything else.
- The defaults, $25,000 at 9% for 180 days, are a placeholder chosen to make the day count effect visible. They are not a rate anyone is offering.
Frequently asked questions
- What is the simple interest formula?
- I = P x R x T. Principal times the annual rate as a decimal times time in years. $25,000 at 9% for 180 days on a 365 day basis is 25,000 x 0.09 x (180/365) = $1,109.59, and $26,109.59 is repaid at maturity. The part that trips people up is T, because a term in days has to be divided by an assumed year length, and US commercial lending often assumes 360 days rather than 365. The same $25,000 over the same 180 days is $1,125.00 on an Actual/360 basis. Terms in months or years are unaffected, since no days were counted.
- What is Actual/360 and why does it cost more?
- Actual/360 means interest accrues at the annual rate divided by 360, charged for the actual number of days elapsed. Because a calendar year has 365 days, a borrower pays 365 days of interest at a rate calibrated to a 360 day year, so the effective rate is 365/360 of the quoted rate, a multiplier of about 1.0139. A 9.00% note accrues at 9.125%, and an 8.00% note at 8.111%: $8,111.11 rather than $8,000.00 on $100,000 for a year. On $1,000,000 at 9% the convention adds $1,250 a year. It is a stated convention rather than a trick, but it makes an Actual/360 quote and an Actual/365 quote non-comparable at face value, which is why this calculator reports the effective rate alongside the interest.
- When is simple interest better than compound interest?
- As a borrower, always, because compounding charges you interest on interest. As a saver, never over a long term, and effectively never either way over a short one. On $25,000 at 9%, simple and monthly compounding are identical to the cent over 30 days, differ by $4.09 over 90 days and by $20.66 over 180 days. Over a full year the gap is $95.17 on $2,250 of interest, and over three years it is $966.13. So under a year the distinction is not worth arguing about, and past a year it is the main thing separating two otherwise identical quotes.
- How do you compare a simple interest deal to a compounding one?
- Convert both to APY, the comparison US law already defines for deposits. Appendix A to 12 CFR Part 1030 gives APY = 100 [(1 + Interest/Principal)^(365/Days in term) - 1], and this calculator applies it automatically. Expect two things. On a term shorter than a year the APY exceeds the stated rate, because annualising assumes the money comes back and is re-earned: 9% over 180 days is an APY of 9.2054%. On a term longer than a year it falls below, because a deal that never compounds loses ground against the annualised standard: 9% simple over three years is an APY of 8.2932%. At exactly 365 days the two are equal, and that is the only term where they agree.
- Is a merchant cash advance simple interest?
- No, and this is the most common misuse of a simple interest calculator in payments. An advance is priced with a factor rate, a flat multiplier that contains no time at all. A 1.30 factor on $50,000 means $65,000 is repaid, and the charge is the same $15,000 whether repayment takes six months or eighteen. So there is no rate to enter here and no term to divide by, and the answer this page would give you is arithmetically valid and financially meaningless. Because the price does not move with speed, the annualised cost swings enormously: the same 1.30 factor is roughly 111% APR when a 10% holdback clears it in about 137 banking days, and roughly 37% when it stretches over eighteen months. Use the merchant cash advance calculator, which solves for the rate that makes the cash you actually received equal the stream of daily payments.
- How do I calculate daily interest on a loan?
- Under simple interest the daily accrual is constant: principal times the annual rate divided by the day basis. $25,000 at 9% on a 365 day basis accrues 25,000 x 0.09 / 365 = $6.16 a day, every day of the term. On a 360 day basis it is $6.25 a day, which is where the extra cost of that convention comes from. This calculator shows the per-day figure directly. If a lender quotes a per diem that rises over the term, the loan is not simple interest regardless of how it is described, and you want the compound interest calculator instead.
Go deeper
Other calculators
Before you borrow against your receivables, check what the processing is costing
Short-term borrowing is usually a response to a cash flow gap, and for a card-accepting business that gap is normally made of two things: what the processor takes, and how long it holds the rest. Both are fixable without signing a note. Compare the major US processors on pricing model, payout speed and reserve policy first.
Looking for something else? See free payment tools and calculators.