Simple Daily Interest Calculator: How Daily Interest Works and How to Work It Out
Introduction
Most interest is quoted per year, but most loans charge it by the day. A mortgage, a student loan, and many personal loans accrue interest daily on the outstanding balance, which means the number of days since your last payment changes the interest you owe, even when the annual rate never moves. Understanding simple daily interest is therefore not a textbook exercise, it is the key to reading a loan statement, checking a payoff figure, and knowing why paying a few days early actually saves money.
This guide explains simple daily interest from first principles: the annual rate, the daily rate, the day count convention, and the formula, with worked examples for loans and savings, the common mistakes, and the difference from compounding. The free Simple Interest Calculator on this site handles annual simple interest, and the daily method below extends it to the day-by-day reality of real loans.
What simple interest means, and what daily adds to it
Simple interest is interest charged only on the original principal, never on interest already earned. The annual formula is familiar: interest equals principal times annual rate times time in years. Investopedia's guide to simple interest states it as I equals P times r times t, where P is principal, r is the annual rate as a decimal, and t is time in years, and its simple versus compound interest guide contrasts it with compounding, where interest earns interest. A 10,000 loan at 6 percent simple interest for one year costs 600 in interest, and the same 600 in the second year if the principal is unchanged, because the base never grows.
Daily simple interest applies the same idea on a daily clock. Instead of charging the annual rate once a year, the lender divides the annual rate by the number of days in the year to get a daily rate, then multiplies that daily rate by the outstanding balance and by the number of days since the last payment or calculation. The interest for a single day is therefore principal times annual rate divided by days in the year. Over 30 days, it is that daily figure times 30, provided the principal does not change in between. When a payment reduces the principal, the daily figure falls from that day onward, which is why extra payments and early payments save interest immediately under daily accrual, not just at the end of the term.
The daily interest formula, step by step
Step 1: Find the daily rate
Divide the annual interest rate, as a decimal, by the number of days in the year. At 6 percent with a 365 day year, the daily rate is 0.06 divided by 365, which is 0.00016438, or about 0.0164 percent per day. At 12 percent with a 360 day year, a convention some lenders use, the daily rate is 0.12 divided by 360, which is 0.00033333. Keep the daily rate unrounded for the calculation and round only the final money figure to cents.
Step 2: Multiply by the balance
Daily interest equals outstanding balance times daily rate. On a 10,000 balance at 6 percent over 365 days, daily interest is 10,000 times 0.00016438, which is 1.64 dollars a day, more precisely 1.6438 dollars. On a 250,000 mortgage balance at 5 percent, daily interest is 250,000 times 0.05 divided by 365, which is 34.25 dollars a day. That daily figure is the cost of carrying the balance for one more day, and it is a useful number to know: it tells you what a week of delay costs, and what a payment saves.
Step 3: Multiply by the days
Interest for a period equals daily interest times the number of days in the period, provided the balance is unchanged. For the 10,000 loan over 30 days: 1.6438 times 30 equals 49.32 dollars. Over a full 365 day year: 1.6438 times 365 equals 600 dollars, which matches the annual simple interest formula, as it must. If the balance changes during the period, split the period at the payment date and calculate each part separately, then add them.
Worked examples: loan, savings, and a mid-period payment
Example one, a personal loan: 8,000 borrowed at 9 percent simple daily interest, 365 day year, no payment for 45 days. Daily rate: 0.09 divided by 365 equals 0.00024658. Daily interest: 8,000 times 0.00024658 equals 1.9726 dollars. Interest for 45 days: 1.9726 times 45 equals 88.77 dollars. Total owed after 45 days, before any payment, is 8,088.77 dollars. Notice that the calculation uses the actual number of days, not months: 45 days is not one and a half months in this method, it is 45 daily charges.
Example two, savings: 5,000 deposited at 4 percent simple daily interest for 90 days. Daily interest: 5,000 times 0.04 divided by 365 equals 0.5479 dollars a day. Interest for 90 days: 0.5479 times 90 equals 49.32 dollars. The deposit is worth 5,049.32 dollars after 90 days if interest is paid out rather than added to the balance. If interest is added to the balance and then earns interest itself, that is no longer simple interest, it is compounding, and the figure will be slightly higher, by the interest on 49.32 dollars for the remaining period, a small difference over 90 days and a large one over years.
Example three, a payment mid-period: 12,000 at 7.5 percent, 365 day year. For the first 20 days, daily interest is 12,000 times 0.075 divided by 365, which is 2.4658 dollars a day, giving 49.32 dollars for 20 days. A payment of 2,000 on day 20 reduces the balance to 10,000, plus the 49.32 dollars of accrued interest, depending on how the lender applies payments, usually to interest first, then principal. For the next 10 days on a 10,000 balance, daily interest is 10,000 times 0.075 divided by 365, which is 2.0548 dollars a day, giving 20.55 dollars. Total interest for 30 days is 49.32 plus 20.55, which is 69.87 dollars, less than the 73.97 dollars that would have accrued with no payment, a saving of 4.10 dollars from paying 20 days in, which is exactly the point of paying early.
| Situation | Daily interest | Period interest |
|---|---|---|
| 10,000 at 6 percent, 365 days | 1.64 dollars a day | 49.32 dollars over 30 days; 600 dollars over a year |
| 8,000 at 9 percent, 365 days | 1.97 dollars a day | 88.77 dollars over 45 days |
| 5,000 at 4 percent, 365 days | 0.55 dollars a day | 49.32 dollars over 90 days |
| 250,000 at 5 percent, 365 days | 34.25 dollars a day | 1,027.40 dollars over 30 days |
| 12,000 at 7.5 percent, payment on day 20 | 2.47 dollars, then 2.05 dollars a day | 69.87 dollars over 30 days with the payment |
365 days, 360 days, and actual day counts
The day count convention is the fine print that changes the answer. Most consumer loans in the United States use actual days over 365, meaning the actual number of days elapsed divided by 365, even in a leap year, when some lenders still use 365 and others use 366 for that year. Some commercial loans use 30 over 360, meaning every month is treated as 30 days and the year as 360 days, which makes monthly calculations tidy but charges slightly more per day than a 365 day year at the same annual rate: at 6 percent, the 360 day daily rate is 0.06 divided by 360, which is 0.00016667, versus 0.00016438 on a 365 day basis, about 1.4 percent higher per day. Your loan agreement states the convention, usually in a sentence about interest accruing daily, and it is worth finding, because using the wrong denominator is the commonest reason a home calculation disagrees with a lender statement by a few dollars.
Leap years deserve a note. Under actual over 365, a leap year still divides by 365, so the daily rate is unchanged and the year simply has one extra day of accrual, 366 days of interest instead of 365. Under actual over 366 in a leap year, the daily rate falls slightly for that year. Under 30 over 360, leap years are ignored entirely. None of these is a trick, they are conventions, but they mean that two loans at the same annual rate can cost different amounts over the same calendar period, and the difference is entirely in the denominator. When comparing loans, compare the daily rate and the convention, not just the headline annual rate.
Simple daily interest versus compound interest
Simple daily interest and daily compounding sound similar and are not the same. In simple daily interest, each day's interest is calculated on the principal, or on the outstanding balance after payments, but unpaid interest does not itself earn interest, unless the agreement capitalises it, for example by adding it to the balance at a month end. In daily compounding, each day's interest is added to the balance, so the next day's interest is calculated on a slightly larger base, and the balance grows exponentially, slowly at first and then faster. Over a month the difference is small, over years it is large, which is why credit cards, which compound, cost far more than a simple interest loan at the same nominal rate.
A concrete comparison: 10,000 at 12 percent for one year. Simple interest gives 1,200 dollars, total 11,200 dollars. Daily compounding gives 10,000 times one plus 0.12 divided by 365, raised to the power 365, minus 10,000, which is about 1,274.75 dollars, total about 11,274.75 dollars, roughly 75 dollars more. Monthly compounding gives about 1,268.25 dollars. The gap grows with rate and time: at 20 percent over five years, simple interest gives 10,000 dollars of interest on 10,000 principal, while daily compounding gives about 17,183 dollars. When a product quotes an annual rate, ask whether it is simple or compound, and how often it compounds, because those two facts matter more than a small difference in the rate itself.
APR, APY, and the rate you are actually paying
APR, annual percentage rate, is the yearly cost of borrowing expressed as a percentage, including certain fees in many jurisdictions, and it is designed to make loans comparable. APY, annual percentage yield, is the effective yearly return on savings when compounding is included, and it is always at least as high as the nominal rate when compounding exists. A savings account quoting 4 percent nominal with monthly compounding has an APY of about 4.07 percent. A loan quoting 6 percent simple daily interest has an effective cost close to 6 percent if interest is paid as it accrues, but higher if interest is capitalised and then earns interest. The headline rate alone never tells the full story: the compounding frequency, the day count, and the fees complete it.
For borrowers, the practical check is the daily interest figure on the statement. Divide the interest charged in a period by the number of days and by the average balance, and you get the daily rate the lender actually applied; multiply by 365 and you get the effective annual rate implied by the statement. If that implied rate differs materially from the quoted rate, the difference is fees, capitalisation, or a day count convention, and the lender should be able to explain which. For savers, the check is the APY on the statement, which already includes compounding, and which is the figure to compare across accounts, not the nominal rate.
Mistakes that cost money with daily interest
The first mistake is using months instead of days: dividing an annual rate by 12 and multiplying by months is monthly simple interest, not daily, and it differs by the actual days in each month, February versus March alone is a 10 percent difference in days. The second is forgetting that payments change the daily figure from the payment date, not from the next statement date, so a payment made on the 10th saves interest from the 10th, not from the 1st of next month. The third is using the wrong denominator, 360 instead of 365, which overstates daily interest by about 1.4 percent. The fourth is confusing simple with compound, and assuming interest does not earn interest when the agreement capitalises it monthly. The fifth is rounding the daily rate too early: round only the final cents figure, because rounding a daily rate to two decimal places before multiplying by a large balance and many days creates dollars of error.
The most expensive mistake is timing: paying late. Under daily accrual, every day of delay costs the daily interest figure, which on a large mortgage balance is tens of dollars a day. A payment ten days late on a 250,000 balance at 5 percent costs about 342 dollars of extra interest before any late fee, because the balance stayed higher for ten extra days. Conversely, paying early, or making an extra principal payment, saves from that day onward, not just at the end of the term. Daily interest rewards promptness in a way monthly interest does not make visible, and that visibility is the best reason to understand it.
Frequently asked questions
How do I calculate simple daily interest?
Daily interest equals balance times annual rate divided by days in the year. Multiply that by the number of days at that balance, splitting the period at any payment that changes the balance.
Should I use 365 or 360 days?
Use the convention in your loan agreement. Most consumer loans use actual days over 365. Some commercial loans use 30 over 360, which charges slightly more per day at the same annual rate.
Is daily interest the same as compound interest?
No. Simple daily interest charges only on the outstanding balance, not on unpaid interest, unless the agreement capitalises interest. Daily compounding adds each day's interest to the balance, so interest earns interest.
Why does paying early save interest?
Because daily interest is charged on the balance each day. Reducing the balance on day 10 instead of day 30 removes 20 days of interest on the amount paid, immediately.
How is daily interest different from monthly interest?
Monthly interest divides the annual rate by 12 and ignores the actual days in the month. Daily interest uses the actual number of days, so February and March cost different amounts at the same rate.
What is the difference between APR and APY?
APR is the yearly cost of borrowing, designed for comparing loans. APY is the effective yearly return on savings including compounding, and it is the figure to compare across savings accounts.
The Bottom Line
Simple daily interest is a small formula with large consequences: balance times annual rate divided by days in the year, times days at that balance. Learn your lender's day count, watch the daily figure on your statement, and pay early when you can. Those three habits turn an abstract annual rate into money you can actually save.
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