Calculator
Finance
MathSimple Interest Calculator
Compute simple interest with I=P×R×T, or solve backward for the rate, principal, or time. Get interest and total amount instantly. Free online calculator.
Have feedback? Report bugs, suggest features, or share your thoughts — we read them allWhat is Simple Interest?
Simple interest is the interest you pay or earn that is calculated only on the original principal, never on previously accumulated interest. The interest grows linearly with time rather than exponentially. If you borrow $1,000 at 5% simple interest for 3 years, you pay exactly $50 per year — $150 total — regardless of how that interest has accrued.
Simple interest is used for short-term consumer loans, auto loans, some student loans, Treasury bills (under a year), and many bonds (for the coupon calculation). It is also the natural mental model for everyday situations like splitting a bill that earns interest until payday. Long-term savings and most modern mortgages use compound interest instead, where the curve becomes exponential and the totals are dramatically higher over decades.
Simple Interest Formula
The simple interest formula is the most-used equation in personal finance:
I = P × R × T
A = P + I = P × (1 + R × T)
Where:
- I = Simple Interest (the amount of interest earned or paid)
- P = Principal Amount (the original loan or deposit)
- R = Annual interest rate as a decimal (5% = 0.05)
- T = Time in years (use 0.5 for 6 months, 0.25 for 3 months)
- A = Total Amount = Principal + Interest
Example Calculation
Borrow $10,000 at 5% annual simple interest for 3 years:
- Simple Interest = $10,000 × 0.05 × 3 = $1,500
- Total amount owed at maturity = $10,000 + $1,500 = $11,500. You pay back the same $1,500 of interest no matter when within the period — five years of holding the principal at 5% always means $2,500 of interest.
Common Applications
- Short-term personal loans (under 12 months)
- Most US auto loans (yes, even multi-year ones, calculated daily on the outstanding balance — a hybrid)
- Some federal student loans use daily simple interest on the outstanding balance
- Treasury bills (T-bills) under one year
- Bond coupon payments (the coupon is simple interest on face value)
- Pay-day loans and high-interest cash advances
- Quick mental estimates of interest costs
- Trade credit ('2/10 net 30' early-payment discounts)
Advantages of Simple Interest
- Easy to calculate and verify — every borrower can check the bank's math
- Predictable monthly payments — no compounding surprises
- Lower total interest than compound interest at the same rate (for the same duration)
- Borrower-friendly for short-term loans where the difference from compounding is small anyway
- Transparent and regulator-friendly — the Truth in Lending Act mandates clear simple-interest APR disclosure
Tips for Using a Simple Interest Calculator
- Always convert the percentage to a decimal: 5% becomes 0.05, 12.5% becomes 0.125
- Match the time unit to the rate unit: if the rate is annual, T must be in years (180 days = 0.493 years using actual/365)
- For monthly compounding loans (most mortgages), don't use this formula — switch to compound interest
- Beware of day-count conventions: 30/360 makes a $10,000 6-month loan at 6% cost exactly $300, while actual/365 makes it cost $295.89
- Use this for quick sanity-checks, then verify with your lender's amortization schedule
Simple Interest vs Compound Interest
The fundamental difference: simple interest is calculated only on the original principal forever, while compound interest is calculated on principal PLUS previously accumulated interest. The gap grows exponentially with time. For a $10,000 deposit at 6% over 30 years, simple interest pays $18,000 total interest, while annual compound interest pays $47,435 — over 2.6× more.
- Simple Interest: Interest each period stays exactly the same — flat line growth
- Compound Interest: Interest grows each period as the balance grows — exponential curve
Frequently Asked Questions
Simple interest applies the rate only to the original principal, so the interest amount each period is constant. Compound interest applies the rate to the running balance, so interest is calculated on principal plus all previously accumulated interest. For one year there is no difference — both formulas give the same answer. The gap appears as time grows. A $1,000 deposit at 10% for 1 year pays $100 either way. After 5 years: simple gives $500, compound gives $610.51. After 20 years: simple gives $2,000, compound gives $5,727.50. After 50 years: simple gives $5,000, compound gives $116,390.85 — the compound curve becomes nearly vertical. The practical implication: for short-term loans and bills, simple interest is the right model; for retirement savings and mortgages, compound interest dominates and you must use the right formula or you'll be off by huge amounts.
Three reasons. First, regulatory simplicity: the Truth in Lending Act in the US requires lenders to disclose interest in a standardized way, and simple interest gives a clear, comparable number that doesn't depend on payment timing tricks. Second, fairness for borrowers: a borrower paying off an auto loan early shouldn't be punished for the compounded interest they would have paid; daily simple interest on the outstanding balance means you save interest by paying early. Third, it matches short-term reality: for loans under a year, simple and compound differ by negligible amounts — a $10,000 loan at 5% for 6 months pays $250 either way, give or take a few cents. Where compound interest dominates — long mortgages, retirement accounts — banks do use it, but they call it 'amortization' or 'compound interest' explicitly and disclose the APY/APR separately.
Day-count conventions decide how many days a loan period contains, which affects the interest. Actual/365 (also called 'actual/actual') counts the literal number of days and divides by 365 — so a January-to-July loan counts 181 days, giving T = 181/365 = 0.4959. 30/360 pretends every month has exactly 30 days, so January-to-July counts 6×30 = 180 days and T = 180/360 = 0.5 exactly. These look almost identical but matter for institutional finance: bonds typically use 30/360 (called 30E/360 or '30 days each month, 360-day year'), money markets use actual/360, credit cards and consumer loans usually use actual/365. The convention can change a $10,000 / 6-month / 5% interest charge by $1-3 — small for individuals but huge across a multibillion-dollar bond portfolio. Always check the day-count convention in the loan or bond contract.
Convert the time to a fraction of a year and plug into I = P × R × T. For 6 months: T = 0.5, so $10,000 at 5% for 6 months = $10,000 × 0.05 × 0.5 = $250. For 90 days: T = 90/365 ≈ 0.247, so $10,000 × 0.05 × 0.247 ≈ $123.29 (under actual/365) — or if using 30/360, T = 90/360 = 0.25 exactly, giving $125. For weeks, divide by 52; for months, divide by 12 if you want monthly-equivalent or use actual day counts for daily precision. The pitfall: if your rate is quoted as 'monthly' (like a credit card's 1.5% per month), don't convert again — multiply directly by the number of months. Always check whether the rate is annual or periodic before doing the math, or you'll be off by 12× or 365×.
Yes — I = P × R × T can be solved for any one variable when the others are known. To find the rate: R = I / (P × T). If you paid $300 interest on a $5,000 loan over 1 year, the rate was 300 / (5000 × 1) = 0.06 = 6%. To find the principal: P = I / (R × T). If you want $500 of interest at 4% over 2 years, you need P = 500 / (0.04 × 2) = $6,250. To find the time: T = I / (P × R). For $1,000 of interest on a $10,000 loan at 5%, T = 1000 / (10000 × 0.05) = 2 years. This rearrangement is the bread-and-butter of basic financial planning — anyone who can do middle-school algebra can solve any simple-interest problem in any direction. The same flexibility does NOT exist for compound interest, where solving for time or rate requires logarithms.
Most consumer 'simple-interest' loans in the US are technically daily simple interest on the outstanding balance — meaning interest is recalculated every day using I = balance × rate / 365, and any extra payment immediately reduces the balance (and thus the next day's interest). This is how most US auto loans, federal student loans (subsidized and unsubsidized), HELOCs, and many personal loans work. Pure simple interest (one calculation at the end of the term) is rare in modern consumer lending — you mostly see it in Treasury bills (the discount is the interest), bond coupons (the coupon rate × face value is the periodic interest, paid out and not compounded), short-term commercial paper, and informal IOUs. Mortgages, savings accounts, and credit cards all use compound interest — even when they advertise 'simple interest' as a feature, it usually means 'daily simple interest on the outstanding balance', not 'one big calculation at maturity'.
The Rule of 72 — divide 72 by the rate to get doubling time — is a compound-interest shortcut. For simple interest, the equivalent rule is the Rule of 100: divide 100 by the rate to get doubling time. At 5% simple interest your money doubles in exactly 100/5 = 20 years (because at 5% per year you earn 5% × 20 = 100% of the principal). At 8%, doubling takes 12.5 years (vs 9 years with compound). At 10%, simple doubles in 10 years (vs 7.27 years with compound). This is the rule that makes simple-interest savings unattractive long-term: at 5%, simple gives you 2× after 20 years and 3× after 40 years, while compound gives you 2.65× after 20 years and 7.04× after 40 years. The math is precisely why every financial advisor pushes compound-interest investments for retirement.
Simple interest grows linearly with time — every additional year adds exactly P × R more interest, no matter how long the loan has been running. After 1 year at $1,000 / 10%, you owe $1,100. After 10 years, $2,000. After 100 years, $11,000. After 1,000 years, $101,000. The curve is a straight line, not a curve. This is the fundamental difference from compound interest: an immortal lender at 10% compound would have $13.78 quintillion after 1,000 years from the same $1,000 — basically all the wealth on Earth, by orders of magnitude. The 'eighth wonder of the world' Einstein quote refers to this exact contrast. In real life almost no loan runs that long, but the math explains why every endowment, pension fund, and sovereign wealth fund obsesses about compounding: a few percent of extra return per year, compounded over decades, dominates everything else they do. Simple interest is the everyday workhorse; compound interest is the long-term miracle.
Yes. Use the 'Solve for' selector at the top to pick which unknown you want. Leave it on 'Interest (forward)' to compute interest and total from principal, rate, and time — the classic I = P × R × T. Switch it to 'Interest rate' to enter the principal, the interest you paid (or earned), and the time, and the tool returns R = I / (P × T) as an annual percentage. Choose 'Principal' to find P = I / (R × T) — how much you must invest to earn a target interest amount. Choose 'Time period' to find T = I / (P × R), in whatever unit you select (days, weeks, months, quarters, or years). This is the same algebraic rearrangement explained in the FAQ above, now built right into the calculator so analysts, lenders, and borrowers can work the equation in any direction without doing the math by hand.
FINANCIAL CALCULATORS22
WUTOOLS