What is simple interest?
Simple interest is the oldest interest formula there is. You pay (or earn) the same amount every year, calculated against the original principal — never against interest that's already piled up. The formula is short: I = P × r × t. Three letters, one multiplication. Most people learn it in school and then never see it again, because banks moved to compounding centuries ago.
But simple interest is still alive in three corners of the modern financial world: most auto loans in the US, short-term Treasury bills, some personal loans that explicitly say "simple interest" in the paperwork, and almost every homework problem in every algebra textbook. Knowing the difference between simple and compound matters — if you assume one and the other applies, your numbers can be off by tens of thousands of dollars over a long horizon.
The formula
Here it is in one line:
I = P × r × t
I = interest earned. P = principal (starting amount). r = annual interest rate as a decimal (5% = 0.05). t = time in years.
To get the total balance at the end, add the interest back to the principal:
A = P + I = P × (1 + r × t)
That's the whole math. No exponents, no logarithms, no monthly-versus-annual conversion if you stay in years. The unit on time matters — r and t must use the same unit. If r is annual, t is in years. If t is in months, divide by 12. If t is in days, divide by 365.
How to use the Simple Interest Calculator
Three inputs, no Calculate button. Type and the answer updates.
- Enter the principal — the amount you're lending, borrowing, or investing. The unit is whatever currency you want; the math doesn't care.
- Enter the annual interest rate as a percentage. Type 5 for 5%, not 0.05. The calculator converts to a decimal internally.
- Enter the time and pick the unit. Years is the default and the most common. Months and days are there for short-term loans and money-market notes.
- Read two numbers: the interest earned (I) and the final balance (A). Below the result, the formula is shown with your values plugged in — useful if you're checking homework or auditing a loan statement.
Your numbers stay in the browser. Nothing's sent anywhere, nothing's saved between sessions. Refresh and you start with a blank slate.
A worked example
You lend a friend $5,000 to start their food truck. They agree to pay simple interest at 4% annually, repaid in full at the end of 3 years. How much do they owe at the end?
- P = $5,000
- r = 0.04 (4% as a decimal)
- t = 3 years
- I = 5,000 × 0.04 × 3 = $600
- A = 5,000 + 600 = $5,600
They pay you $5,600 at the end of year three. The interest is $200 per year, every year, calculated against the original $5,000 — even though the loan balance is conceptually growing each year, the simple-interest formula ignores that.
Now compare to compound interest on the same loan. If interest compounded annually, the balance would be 5,000 × (1.04)^3 = $5,624.32. The extra $24.32 is what compounding adds over three years at this rate. Small over short horizons. Enormous over long ones.
Simple vs compound: when each matters
The gap between simple and compound interest depends almost entirely on time. Over a year or two the difference is small enough to round away. Over thirty years it can be more than the principal itself. Here's the same $10,000 at 5% interest under both methods:
| Time | Simple interest (total) | Compound interest (annual, total) | Gap |
|---|---|---|---|
| 1 year | $10,500 | $10,500 | $0 |
| 5 years | $12,500 | $12,763 | $263 |
| 10 years | $15,000 | $16,289 | $1,289 |
| 20 years | $20,000 | $26,533 | $6,533 |
| 30 years | $25,000 | $43,219 | $18,219 |
Year one is a tie. By year thirty, compounding has more than doubled the simple-interest gain. The mechanism is straightforward: each year compound interest earns interest on the previous year's interest, while simple interest forgets that those gains existed and starts fresh from the original principal.
For investments, you almost always want compounding — and you usually get it automatically. Savings accounts compound daily. Index funds compound continuously through reinvested dividends and price growth. For loans, the picture flips. Simple interest favors the borrower because it caps how fast the debt grows. That's why auto loans, which use simple interest calculated daily on the outstanding balance, are often a better deal than credit cards, which compound aggressively.
Where simple interest actually shows up
It's more common than the textbook frames it. A few real-world places where the formula on this page applies cleanly:
- Most US auto loans. Interest is calculated daily on the current outstanding balance using the simple-interest formula. Paying early reduces the balance and immediately reduces future interest — no prepayment penalty math.
- US Treasury bills (T-bills). Short-term government debt (4, 8, 13, 26, or 52 weeks). Sold at a discount; the difference between purchase price and face value is the simple interest earned.
- Some personal loans. If the loan paperwork explicitly says "simple interest" and lists a fixed daily rate, the math here applies. If it doesn't say that, assume amortization (compound) and use a different calculator.
- Most bonds at par. The coupon payments are simple interest on the face value. Bond pricing itself involves more math, but the coupon math is clean simple interest.
- Promissory notes between people. When you write up a private loan to a family member or friend, simple interest is the default — easier to calculate, easier to be fair about, easier to explain.
Where it doesn't apply: savings accounts (compound), CDs (compound), mortgages (amortized — a specific type of compound), credit cards (compound, daily), and almost every modern investment product. If your bank told you a rate, it's almost certainly compounding behind the scenes.
Months and days: handling short time periods
The formula expects time in years, but a lot of real situations are measured in months or days. Convert by dividing.
Months → years: t (years) = months / 12
Days → years: t (years) = days / 365
Worked example: you take a 6-month short-term loan of $1,000 at 5% simple interest. The interest is:
- I = 1,000 × 0.05 × (6 / 12) = 1,000 × 0.05 × 0.5 = $25
For a 90-day T-bill at the same rate on the same principal:
- I = 1,000 × 0.05 × (90 / 365) = 1,000 × 0.05 × 0.2466 = $12.33
This calculator handles the conversion when you pick the unit — type the number, pick "months" or "days," and the answer adjusts. Banks sometimes use 360-day years (the "banker's year") for short-term commercial calculations, which makes the daily rate slightly higher; for personal and retail purposes, 365 days is the standard and what this tool uses.
APR, APY, and what to type in the rate field
Three rate names get confused all the time. They are not the same number.
- Interest rate — the nominal annual rate. This is what the formula wants.
- APR (Annual Percentage Rate) — for loans, this typically includes fees and is mandated by the Truth in Lending Act. For a pure simple-interest loan with no fees, APR equals the interest rate. For a loan with origination fees, APR is higher than the stated rate.
- APY (Annual Percentage Yield) — for savings, this is the effective annual rate after compounding. A 5% nominal rate that compounds daily has an APY of about 5.13%. The APY is always equal to or higher than the nominal rate (equal only when there's no compounding).
For this calculator, type the nominal annual rate. If your loan paperwork lists APR and no fees, use that. If it lists a "simple interest rate," use that directly. If your savings account shows APY, you're using the wrong calculator — APY is a compounding concept, not a simple-interest one.
Frequently asked questions
Why doesn't simple interest match what my bank tells me?
Because your bank is almost certainly compounding. Even savings products that advertise "simple interest" usually compound daily, which is mathematically very close to continuous compounding. The pure simple-interest formula on this page is the textbook version. For investments, the real-world version is a small win for you. For loans, it's a small win for the lender. Either way, if the product compounds, use a compound interest calculator instead.
Can I use this for my mortgage?
No. Mortgages use amortization, which is a specific compound-interest formula that calculates a constant monthly payment split between interest and principal. Early in the loan, most of the payment goes to interest; late in the loan, most goes to principal. The simple-interest formula here will significantly underestimate the total interest paid on a mortgage. Use the Amortization Calculator or the Mortgage Payoff Calculator instead.
What about credit cards?
Credit cards compound daily, often at rates of 20-30% APR. The simple-interest formula on this page will dramatically underestimate the cost of carrying a credit card balance. A $5,000 balance at 22% APR compounded daily for one year accumulates about $1,228 in interest — significantly more than the $1,100 you'd get from the simple-interest formula. Pay credit card balances in full each month; if you can't, the credit card is the financial product to attack first.
How do I solve for the rate or the time?
Rearrange the formula. To find the rate given I, P, and t: r = I / (P × t). To find the time given I, P, and r: t = I / (P × r). To find the principal needed to earn a target I at rate r over time t: P = I / (r × t). All four versions are just the same equation with a different variable isolated. For these inversions you may find the Percent Error Calculator useful for sanity-checking your work.
Does this work in any currency?
Yes — the formula is unit-agnostic. Pounds, euros, yen, pesos, rupees, dollars: type the number, get a result in the same unit. The calculator doesn't convert currencies; it just does the math on whatever number you give it.
What happens if the rate or time is negative?
Mathematically, a negative time means going backward — finding the principal that, at a given rate, grows into the current amount. A negative rate is unusual but real (some European bonds during the 2010s had negative yields). The formula handles both cleanly, but the calculator clamps inputs to non-negative values for the common case. If you actually need negative-rate math, do it by hand: the formula doesn't change.
Why is the answer the same every year?
That's the definition of simple interest. The interest earned in year one is P × r. The interest earned in year two is also P × r — because the formula uses the original principal, not the principal-plus-interest. By year ten, you've earned P × r ten times, which is P × r × 10. The same flat amount every year is what makes it "simple."
Is this calculator accurate enough for real financial decisions?
For simple-interest products (T-bills, bonds at par, simple-interest auto loans, private notes between people), yes — the formula is exact, no approximation. For anything that compounds, use a tool built for that math. Using simple interest on a compounding product will always underestimate the real number, sometimes by a lot.