Simple Interest Calculator
The textbook interest formula, computed honestly: I = P·r·t, where only the principal ever earns interest. Enter the principal, the annual rate, and the time — in years or in months, converted exactly as months ÷ 12 — to get the interest and the total. Fair warning up front: most real savings accounts and loans compound instead; this tool is for the textbook problems and the contracts that genuinely use simple interest.
Principal, rate, and time
Example: 1,000 at 5% for 3 years → interest 150, total 1,150; 1,000 at 4% for 18 months → interest 60.
Simple interest is the counterpart to compound growth. The companion guide ROI and CAGR explained works through what changes once interest starts earning interest — the behaviour this page leaves out by design — and sits alongside the rest of the Sumvia guides.
The formula, worked through
I = P × r × t with the rate as a decimal and the time in years. The worked example — 1,000 at 5% for 3 years — is 1,000 × 0.05 × 3 = 150, for a total of 1,150; both figures were computed at build time by the same engine behind the form. Months convert exactly before the multiplication: 18 months is t = 1.5, never a rounded 1.4 or 1.6, which is how 1,000 at 4% for 18 months lands on precisely 60. Simple interest is linear — double the time, double the interest — and that linearity is its defining difference from compounding.
Linearity is worth seeing on the numbers, because it is what makes simple interest predictable in a way compounding never is. Each of the three inputs scales the interest in exact proportion, one at a time. Hold the example's rate and principal and double the time from 3 to 6 years, and the interest doubles from 150 to 300; halve it to 1.5 years and the interest halves to 75. Double the rate instead, from 5% to 10% over the same 3 years, and the interest again doubles, to 300. Double the principal, from 1,000 to 2,000, and it doubles once more, to 300. There is no cross-term and no feedback: nothing the interest earns is ever fed back into the base, so a graph of interest against any one input is a straight line through the origin. That is the whole content of the word simple.
Reading the interest and the total
The tool returns two figures, and keeping them straight matters more than the arithmetic does. The interest (I) is the charge or earning on its own — 150 in the example. The total (P + I) folds the principal back in — 1,150 — and is the single number that changes hands at the end of the term. Which one you want depends only on the direction of the money: on a deposit the total is the balance you would withdraw; on a borrowing the total is the amount repaid, of which 150 is the cost of the loan and 1,000 is simply the principal coming back. Quoting the total where you meant the interest overstates the cost or return by the whole principal, which is why the form shows both and labels each rather than leaving you to subtract. When the rate is 0% the two figures coincide: 1,000 at 0% for 5 years returns 0 interest and a 1,000 total, the principal unchanged — the plain check for a genuinely interest-free period.
Months, years, and exact conversion
Time can be entered in years or in months, and the choice is a convenience, not a different calculation. Months are converted to years as t = months ÷ 12 before anything is multiplied, so the conversion is exact and carries no day-count convention: 18 months is 1.5 years to the engine, and entering 1.5 years directly gives the identical 60 interest that 18 months does. Fractions are accepted in either unit — 2.5 years, 4.5 months — and because the formula is linear, a fractional term simply scales the interest by that fraction of a year. The exact division is also why a term that is not a whole number of years can produce a long decimal: 1,000 at 5% for 4 months is t = 0.333333 of a year, and the interest works out to 16.666667 — a repeating decimal the tool shows to six places rather than rounding off early. No calendar, leap year, or day-count basis enters into it; the textbook formula has no need of one, and inventing one here would only disagree with the contracts that genuinely use it.
Simple versus compound, honestly
Simple interest pays on the principal alone, forever. Compound interest pays on the principal plus accumulated interest, so the balance grows faster every period — and most financial products in the wild (savings accounts, credit cards, mortgages) compound. Use this page when the arrangement actually specifies simple interest: homework and exam problems, many short-term and auto loans, judgment interest, accrued bond interest, or a written agreement between individuals. When your question is compound — "what annual rate turns 10,000 into 15,000 in five years?" — that is the CAGR calculator's territory, and percentage changes without a time dimension belong to the percentage calculator.
The engine itself enforces the distinction rather than papering over it. Its only interest function is this one; there is no hidden compound mode, and no setting flips it into period-by-period accrual. That is deliberate. A single form that silently switched formulas would be the easiest possible way to quote the wrong figure with full confidence — so the interest here never earns interest, the page says so plainly, and the compound questions are sent to the tools built for them. If what you are modelling grows on its own output, this is the wrong page, and the straight line it draws is exactly the sign that tells you so.
The misreadings that produce a wrong number
Nearly every wrong answer from a correct formula traces to one of a few input habits, and all of them are visible once you know to look. The rate is a percent, not a decimal. The field is labelled annual interest rate (%), and the engine divides by 100 for you, so a 5% rate is entered as 5. Enter it as 0.05 and the engine reads 0.05%, turning the example's 150 of interest into just 1.5 — a result a hundred times too small, and a common mistake on interest forms.
The rate is annual. If a contract quotes a monthly rate, it is not this field's input; convert it to a yearly figure first, or the term you enter in months will be multiplied against a rate meant for a single month and understate the interest. The form pairs an annual rate with a time it converts to years precisely so the two always share the same clock. And simple is not compound. If the arrangement compounds, this page will quote less than accrues, by a gap that is small over a few periods and large over many — so match the tool to the contract before trusting the figure.
Finally, the engine refuses rather than guesses when an input has no sensible answer. The principal must be greater than zero, the annual rate may be zero but not negative, and the time must be greater than zero; break any of those and you get a short written message where a number would be, never a NaN, an infinity, or a silently wrong value. This is the same discipline described on the methodology page: undefined operations are reported as such instead of answered.
How the result is rounded and displayed
Internally the calculation keeps the full precision of double-precision arithmetic; what you read is a rounded presentation of a more exact value. Before display, results are normalized to twelve significant digits to strip binary floating-point artifacts, then shown to at most six decimal places. That is why a term like 4 months, which makes t a repeating 0.333333 of a year, yields an interest of 16.666667 on screen rather than a ragged tail of noise digits. A nonzero result too small to survive six decimals is not flattened to "0" either: it falls back to six significant figures, so a deliberately extreme 1 at 0.00004% for one year still reads 0.0000004 rather than vanishing. The practical caution is the one the methodology states — a displayed figure is rounded, so for chained work prefer doing the whole calculation in one pass rather than retyping an intermediate.
The limits are the honest ones of any generic tool. As the methodology page puts it, specific domains — "tax rules, regulated interest calculations, jurisdiction-specific rounding of currency — often impose their own conventions that a generic tool does not know." Simple interest sits squarely under that sentence: a statute or contract may round each period differently, count days on a basis of its own, or define the rate in a way that is not the plain annual percent this engine multiplies. Inputs are also bounded to a documented range (±1015) so the arithmetic stays dependable; a value beyond it is reported as out of range rather than quietly computed with eroding accuracy. The calculator implements the general definition; your jurisdiction's or contract's conventions may differ.
Frequently asked questions
What is the simple interest formula?
I = P × r × t: principal times the annual rate (as a decimal) times the time in years, and the total repaid or received is P + I. For 1,000 at 5% over 3 years, that is 1,000 × 0.05 × 3 = 150 interest and a 1,150 total.
Do I type the rate as 5 or as 0.05?
As 5 — the whole-number percent. The engine divides by 100 internally, so 5 means 5%. Typing 0.05 is read as a rate of 0.05%, and 1,000 for 3 years then earns only 1.5 instead of 150 — a common way this form produces a number that looks a hundredfold too small.
How is simple interest different from compound interest?
Under simple interest, only the original principal ever earns interest, so the charge is the same amount each year and the interest over the example's 3 years at 5% is just 150 in total. Under compound interest, each period's interest is added to the base and then itself earns, so every period is figured on a larger amount; the two pull apart slowly over a few periods and sharply over many. This engine implements only the simple formula — there is no compound mode — so it cannot produce the compounded figure for comparison; for a compound question, the CAGR calculator is the tool built for it.
Which one does my savings account or loan actually use?
Check the agreement rather than assume. Use this page only when the terms explicitly state simple interest — interest charged on the original principal alone; many common products compound instead, in which case this calculator would understate what actually accrues. If you are unsure which applies, treat the figure here as the simple-interest case and confirm it against the contract’s own wording before relying on it.
How are months handled?
Exactly, as t = months ÷ 12. Eighteen months is t = 1.5 years, so 1,000 at 4% for 18 months earns 1,000 × 0.04 × 1.5 = 60. No day-count convention is involved — the plain formula has no need of one.
Can the rate be zero? Can the time be fractional?
Both. A 0% rate is legal and yields zero interest — useful for checking a promotional no-interest period. Time accepts any positive number of years or months, including fractions like 2.5 years or 4.5 months.
Why was my input rejected?
The engine checks three things before it computes: the principal must be greater than zero, the annual rate may be zero but not negative, and the time must be greater than zero. Fail any of those and it returns a short written message rather than a number. Inputs are also held to a documented magnitude so results stay where double-precision arithmetic is dependable; a figure beyond it is reported as out of range rather than computed.
Where do I go for compound growth?
For the reverse question — what annual compound rate turned a start value into an end value — use the CAGR calculator. This page deliberately does not bolt on a compound mode: mixing the two formulas behind one form is how people end up quoting the wrong number.
Values are computed in your browser and never transmitted. This tool is arithmetic for a stated formula, not financial advice — verify any consequential figure against the actual terms of your agreement, which may compound. Details on the methodology page.