Simple interest calculator
Most saving and borrowing compounds, so simple interest sounds like a textbook curiosity. It is not. When a US federal agency pays an invoice late, the Prompt Payment interest it owes is calculated as principal × rate ÷ 360 × days, with no compounding at all until the payment is more than a month overdue — Treasury publishes the formula and a separate compounding calculator for the longer case. Bond coupons work the same way: a fixed percentage of face value, paid out rather than added back. The distinction matters because a headline rate quoted simply is a different product from the same rate quoted compounding. Over five years at 5% the gap is about a tenth of the interest — 262.82 against 2,500 — and it widens with every year that passes: at ten years it is a quarter, and at twenty it is more than half.
Simple interest is principal × rate × time. Ten thousand at 5% for five years earns 2,500, for a total of 12,500. The same money compounding annually would earn 2,762: the difference is interest on interest.
How to calculate simple interest
The gap between simple and compound interest grows with both time and rate, and it grows non-linearly. Over one year there is no difference at all. Over five years at 5% it is $262.82 against $2,500 of interest, about a tenth. Over thirty years at 8% the compound figure is $90,626.57 against a simple $24,000, nearly four times as much. That asymmetry makes the distinction trivial for a three-month bridging facility and decisive for a pension, and it means a quoted rate is incomplete until a compounding frequency is attached to it.
The per-day row assumes a 365-day year, and the world does not agree
Day-count conventions are where short-dated interest quietly goes wrong. This page divides the annual interest by 365, so $10,000 at 5% shows $1.3699 a day. The US Treasury computes Prompt Payment interest as principal times the rate divided by 360, times the number of days, which on the same money is $1.3889. Over a 90-day facility the two conventions are $123.29 and $125.00, a difference of $1.71 on ten thousand dollars. Run a 360-day daily rate across a real 365-day year and it collects $506.94 rather than $500, an effective 5.0694% from a rate written as 5%. Actual/360 is common in US commercial lending and money markets, actual/365 elsewhere, and 30/360 in parts of the bond market. Before comparing two short-dated quotes, find out which denominator each one is using.
Two different things are called simple interest
On this page it means what the formula says: interest on the original principal, never on interest already earned. Car and mortgage lenders use the phrase differently, for a loan where interest accrues daily on the outstanding balance and every payment is applied to the accrued interest first. That is not a fixed-principal calculation at all, and paying such a loan a few days early genuinely reduces the interest. Reading a lender’s "simple interest" as the arithmetic on this page will produce the wrong number.
What people use it for
- Working out interest on a flat-rate loan
- Calculating bond coupon income
- Checking a short-term lending quote
- Understanding what compounding adds
- Pricing late-payment interest on an unpaid invoice
- Converting an annual rate into a daily accrual for a part-month
Questions
I = P × r × t; principal times annual rate times time in years.
$10,000 at 5% for five years earns $2,500, for a total of $12,500. That is $500 a year, $41.67 a month and $1.3699 a day.
Simple interest is only ever charged on the original principal. Compound interest is charged on the principal plus the interest already added.
$262.82 on the defaults, about a tenth of the interest. The row labelled "Compounding would add" is the annual-compounding figure minus the simple one.
Because there has been no interest to compound yet. Annual compounding and simple interest are the same calculation until the first interest payment has been added.
Thirty years at 8% earns $24,000 simple and $90,626.57 compound. The compound figure is not double the simple one, it is nearly four times it.
Actual/365: the annual interest divided by 365. A lender or agency using actual/360 will quote a higher daily figure from the same rate.
On short horizons, yes. Ninety days on $10,000 at 5% is $123.29 on a 365-day basis and $125.00 on a 360-day one. Across a full year the 360-day convention collects $506.94, an effective 5.0694%.
Late-payment interest on US federal invoices, short-term bridging finance, and bond coupons, which pay a fixed percentage of face value rather than adding it back.
Principal times the interest rate divided by 360, times the number of days. Its own guidance sends anything more than a month late to a separate compounding calculator instead.
Probably, in the lender’s sense of the phrase rather than this page’s. Lenders call a loan simple interest when interest accrues daily on the outstanding balance. That is a declining-balance calculation, not the fixed-principal one here.
Enter years as a decimal; six months is 0.5, eighteen months is 1.5.
Divide the days by 365 and enter the result. Forty-five days is 0.1233. If the agreement uses a 360-day year, divide by 360 instead and accept that the label above says years.
Yes, at the same nominal rate. It is worse for a saver, for exactly the same reason.
The arithmetic runs and returns a negative interest figure. It is a sensible model of a fee expressed as a rate and not much else.
No. Run it twice, once for each period at its own rate, and add the two interest figures. The principal stays the same in both runs, which is the defining feature of simple interest.
Only to sanity-check the order of magnitude. Deposit accounts compound, so the compound interest calculator is the right tool and the difference row here shows what you would be leaving out.