Simple Interest Calculator

Background.

This simple interest calculator solves the single most common equation in introductory finance, I = P x r x t, for whichever variable you don't already know — the interest itself, the principal, the annual rate, or the term in years. Simple interest is the textbook starting point for understanding the time value of money, and unlike compound interest it never pays interest on previously accrued interest. The interest is computed once, on the original principal, and grows in a strictly linear way over the life of the loan or investment.

That property makes it both easy to reason about and surprisingly common in real-world contracts that most people assume must be compounding: short-term consumer loans, most U.S. auto loans documented under the federal Truth in Lending Act, U.S. Treasury bills sold at a discount, many personal lines of credit, payday and pawn-shop loans where state law permits them, and short-dated commercial paper traded in the wholesale money market. Anywhere the term is short or the contract pays out in a single lump sum at maturity, simple interest is usually the right model.

The Consumer Financial Protection Bureau's consumer-loan guidance, the Federal Reserve's H.15 release on selected interest rates, and standard graduate-level finance textbooks such as Bodie, Kane, and Marcus's Investments all introduce the concept in the same way: interest equals principal times the periodic rate times the number of periods, with no recursion and no compounding adjustment. This Quanta calculator implements that formula in arbitrary-precision decimal arithmetic so that rounding errors that show up in spreadsheet-based estimates never appear in the result.

You choose which variable to solve for, supply the other three, and the tool returns the interest, the total amount payable (A = P + I), and the principal-rate-time triple as confirmed values. Use it to size a six-month personal loan, to back-solve the implied rate on a friend-and-family note, to estimate the discount-yield interest on a 26-week T-bill, or to prorate interest for a partial year when a loan is paid off early.

The math is so tractable that it almost feels too simple to need a calculator, but in practice savers and borrowers consistently get it wrong by confusing simple interest with compound interest, by forgetting to convert percentages to decimals before multiplying, or by mixing months and years. The tool below removes all three sources of error.

Below the widget you will find the explicit formula in plain notation, a fully worked example built around the canonical $10,000 / 5% / 3-year textbook problem, five long-tail FAQs answering the questions real users search for — including how simple interest differs from compound, when banks actually use it, how to handle partial-year proration, and how the U.S. Treasury bill bank-discount methodology relates to ordinary simple interest — and primary-source citations to Bodie/Kane/Marcus, Brealey/Myers/Allen, the CFPB, and the U.S. Treasury. Read past the calculator if you want to internalize the formula well enough to estimate any short-term financing decision in your head.

What is simple interest calculator?

Simple interest is the dollar amount earned on a deposit or owed on a loan computed using only the original principal, the stated periodic rate, and the elapsed time — never on any interest that has already accrued. Expressed algebraically, it is I = P x r x t, where P is the principal (the starting amount), r is the rate expressed as a decimal per the same unit of time as t, and t is the term. If the stated rate is annual, t must be in years; if the rate is monthly, t must be in months; the units must agree or the result is meaningless. The total amount payable at maturity is A = P + I, which factors neatly to A = P(1 + rt). What makes simple interest mathematically distinct from compound interest is the absence of recursion. Compound interest reinvests each period's accrued interest into the principal base, so the next period's interest is computed on a larger number — producing exponential growth. Simple interest never folds the accrued interest back into the principal, so the growth is strictly linear. A $1,000 loan at 6% simple interest accrues exactly $60 in year one, exactly $60 in year two, and exactly $60 in year three — for a total of $180. The same loan at 6% compounded annually accrues $60, then $63.60, then $67.42 — a total of $191.02. The gap is small over short horizons and becomes enormous over long ones, which is precisely why simple interest is reserved for short-term contracts in modern finance. When you see a 30-year mortgage, a 401(k), or a high-yield savings account, you can assume it compounds. When you see a 90-day T-bill, a 60-month auto loan, or a 6-month personal loan, it is almost certainly simple-interest math.

How to use this calculator.

1. 01Choose what to Solve For. Default is Interest (the unknown is I in I = P x r x t). Switch to Principal, Rate, or Time if one of those is what you need.
2. 02Enter the Principal — the original amount of the loan, deposit, or investment in dollars. Leave this field alone if you selected Solve For = Principal.
3. 03Enter the Annual Interest Rate as a percentage, not a decimal. For a 5% rate, type 5, not 0.05. Leave this field alone if you selected Solve For = Rate.
4. 04Enter the Term in years, using decimals for partial years. Six months is 0.5, 90 days is roughly 0.2466 (90 / 365). Leave this field alone if you selected Solve For = Time.
5. 05If you are solving for Principal, Rate, or Time, enter the known Interest dollar amount. This field is ignored when Solve For = Interest.
6. 06Read the outputs. Interest is the dollar amount of accrued interest, Total is principal plus interest (A = P + I), and the remaining rows echo or report the solved principal, rate, and term so you can sanity-check the result.
7. 07Use the result. The Total field is exactly what is owed at maturity on a simple-interest loan, or exactly what is paid out at maturity on a simple-interest deposit. There is no further compounding adjustment.

The formula.

The simple interest formula is I = P x r x t, where I is the total interest in currency units, P is the principal in the same currency, r is the periodic interest rate expressed as a decimal (a 5% annual rate becomes 0.05), and t is the time elapsed in the same period as the rate (years for an annual rate). The total amount A repayable at maturity is the principal plus the interest: A = P + I, which can be factored as A = P(1 + rt). When the unknown is not the interest, the same equation is rearranged: P = I / (r x t) when solving for principal, r = I / (P x t) when solving for rate, and t = I / (P x r) when solving for time. This calculator stores the rate as a percentage in the input (e.g. 5 for 5%) and divides by 100 internally before multiplying, which prevents the single most common user error in financial spreadsheets — multiplying by the percent symbol rather than the decimal equivalent. All arithmetic runs through arbitrary-precision Decimal.js, so values rounded to ten decimal places remain exact across the four rearrangements and the unit conversions in fractional-year scenarios. If you choose Solve For = Principal or Solve For = Time with an annual rate of exactly zero, the formula degenerates and the engine returns a clear error rather than infinity, because dividing the interest by a zero rate has no economic meaning.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Bodie, Zvi; Kane, Alex; Marcus, Alan J. — Investments, 12th ed., McGraw-Hill, Chapter 5: Risk, Return, and the Historical Record (introduction of simple vs. compound interest).
2. [2]Brealey, Richard A.; Myers, Stewart C.; Allen, Franklin — Principles of Corporate Finance, 13th ed., McGraw-Hill, Chapter 2: How to Calculate Present Values (simple vs. compound interest, time-value of money foundations).
3. [3]Consumer Financial Protection Bureau — Consumer loan education materials covering simple-interest auto loans, personal loans, and prorated interest disclosures under the Truth in Lending Act.
4. [4]U.S. Department of the Treasury, Bureau of the Fiscal Service — Treasury Bill Auction Results and Discount Yield Methodology (the bank-discount and bond-equivalent yield conventions used for T-bills).
5. [5]Federal Reserve Board, Statistical Release H.15 — Selected Interest Rates (canonical source of short-term U.S. money-market rates against which simple-interest estimates can be sanity-checked).