Simple Interest Calculator
Calculate simple interest from principal, rate, term, and day-count basis, with gross and net maturity totals, payout checkpoints, and an accrual curve.{{ summaryTitle }}
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A flat interest quote is easiest to read when the principal stays fixed. The lender, borrower, student, or analyst can ask one clear question: how much money does the stated annual rate add over the stated time? That is the setting where simple interest belongs. It treats interest as a charge or earning on the original principal, not as a growing balance that earns interest on earlier interest.
The three basic terms are principal, rate, and time. Principal is the amount being lent, borrowed, deposited, or studied. The rate is normally quoted as an annual percentage, even when the term is only a few weeks or months. Time has to be turned into a fraction of a year before the formula can be used. A six-month quote at 8% is not an 8% return; it is roughly half of that before fees, tax effects, or withholding because the money is exposed for half a year.
Day-count basis is the part many quick estimates hide. A daily quote can divide by 365, 360, or another convention named in the agreement. The percentage rate may be identical, but a smaller day-count denominator gives a larger year fraction for the same number of calendar days. That difference is small on a short, low-rate example and more noticeable on larger principal amounts, longer terms, or higher rates.
Simple interest is useful for classroom problems, late-payment estimates, short notes, flat-rate comparisons, and deposits or loans that do not add interest back into the principal. It is a poor substitute for products that amortize, compound, charge periodic fees, capitalize unpaid interest, or change principal after payments. A quote that uses the word interest is not automatically a simple-interest quote, so the stated convention matters as much as the rate.
| Term | Plain meaning | Common mistake |
|---|---|---|
| Principal | The base amount used for the interest calculation. | Using principal plus unpaid interest when the quote is meant to stay flat. |
| Annual rate | The yearly percentage applied to the principal. | Reading a six-month result as though the full annual percentage was earned. |
| Term | The length of time the principal accrues interest. | Mixing months, days, and weeks without converting them to a year fraction. |
| Day-count basis | The convention used to turn days into part of a year. | Comparing offers that use different denominators as if they were identical. |
| Withholding | A portion removed from interest before the net amount is kept. | Treating the gross maturity amount as spendable cash when withholding applies. |
How to Use This Tool:
Enter the quote or example in the same units used by the agreement, then compare the maturity amount with the schedule and warnings before relying on the number.
- Enter the Principal as a positive dollar amount. If the page asks you to check the inputs, fix the principal before reading the results.
- Enter the Annual simple rate as a percent, such as 6.25 for 6.25% per year. Do not enter the decimal form.
- Set the Term and choose years, months, weeks, or days. The summary should show the converted years beside the selected day-count basis.
- Choose the Day-count basis that matches the quote. Use Actual / 365 for a general estimate unless the agreement says Actual / 360 or 30 / 360.
- Open Advanced when you need payout checkpoints, a start date, interest withholding, or a scenario label. The start date only affects projected checkpoint dates, not the interest formula.
- Read Interest Snapshot first, then compare the Payout Ladder, Decision Guide, Guide Markers, and Accrual Curve when the schedule or sensitivity checks matter.
- Copy or download the table, chart, or JSON output only after the warnings and basis choice match the agreement you are checking.
If the result disappears or a warning appears, start with the required inputs: principal above zero, a non-negative annual rate, and a term above zero.
Interpreting Results:
The gross interest is the amount earned or owed before withholding. The gross maturity amount adds that interest to principal. When withholding is entered, net interest subtracts the withheld portion, and net maturity amount adds only the remaining interest to principal.
Daily accrual is an average under the selected basis, not a daily compounding rate. Gross yield on principal is the interest for the entered term divided by the principal, so it should not be read as annual percentage yield. The Accrual Curve should rise evenly because simple interest adds the same amount for equal fractions of time.
- Verify the day-count basis before comparing two offers with the same headline rate.
- Use the Payout Ladder as a checkpoint schedule, not as proof that interest is reinvested or paid out.
- Treat high-rate and very-long-term warnings as stop-and-check signals because many real products use different math.
- Use the Decision Guide and Guide Markers to see how a one-point rate move, one extra term unit, withholding, and basis changes affect the result.
Technical Details:
Simple interest has a linear shape because the principal does not change during the calculation. Every output begins with the same year fraction: the entered term is converted to years, the annual rate is converted from a percentage to a decimal, and the product of those values gives gross interest.
Formula Core
P is principal, r is annual rate as a decimal, t is the year fraction, I is gross interest, A is gross maturity amount, w is withholding as a decimal, and N is net maturity amount.
For a $15,000 principal at 6.25% for 18 months, the year fraction is 1.5. Gross interest is 15,000 x 0.0625 x 1.5, or $1,406.25. With 10% withholding, $140.63 is removed from interest, leaving a net maturity amount of $16,265.63 after cent rounding.
| Basis or unit | Year-fraction rule | Result effect |
|---|---|---|
| Years | Entered years are used directly. | Two years means t = 2.0000 before rounding for display. |
| Months | Months are divided by 12. | Month terms are calendar-neutral estimates, so 18 months means t = 1.5000. |
| Weeks | Weeks become seven-day spans, then are divided by 365 or 360. | The selected day-count basis changes the year fraction. |
| Days with Actual / 365 | Days are divided by 365. | Common for consumer-style daily accrual estimates. |
| Days with Actual / 360 | Days are divided by 360. | The same day count produces slightly more interest than Actual / 365. |
| 30 / 360 | Months are treated as 30 days and years as 360 days. | Useful only when the agreement, worksheet, or market convention calls for it. |
The schedule divides the final gross and net interest across the selected number of checkpoints. Each row uses a fraction of the total term, so a halfway checkpoint shows roughly half of the final simple interest. The chart samples the same checkpoint path and draws gross interest, net interest, and withheld interest as separate line series.
| Derived value | How it is derived | Use with care when |
|---|---|---|
| Daily accrual | Gross interest divided by the rounded day count. | The quote compounds daily or uses lender-specific posting rules. |
| Monthly-equivalent accrual | Gross interest divided by total years times 12. | The product actually has unequal calendar months or payment dates. |
| Gross yield on principal | Gross interest divided by principal. | You need an annualized yield or annual percentage yield. |
| Rate-point impact | Principal times year fraction times 1.00%. | You are comparing quotes with different compounding or fee terms. |
| Basis shift | Interest difference between the selected basis and the alternate actual-day basis. | The agreement uses a convention outside Actual / 365, Actual / 360, or 30 / 360. |
Displayed money values are rounded to cents. Percent displays can show extra decimals so the year fraction and yield are easier to audit. Inputs are bounded for stability: principal is capped at $1,000,000,000,000, annual rate at 1,000%, term at 1,000,000 units, and withholding from 0% to 100%.
| Warning or validation | Reason to check it |
|---|---|
| Principal above 0 is required | A zero or negative base amount cannot produce a useful maturity estimate. |
| Annual rate cannot be negative | The calculation covers ordinary positive simple interest, not negative-yield products. |
| Term above 0 is required | No time means no meaningful accrual path. |
| Annual rates at or above 50% | High rates often signal fees, penalties, risk pricing, or terms that deserve closer review. |
| Terms of about 30 years or longer | Long horizons are commonly modeled with compounding, amortization, or contract-specific rules. |
Privacy and Accuracy Notes:
The calculation uses the numbers entered in the browser. It does not look up a bank account, pull a credit report, or verify a contract. If you share or bookmark a URL after changing inputs, the visible scenario values may be included in the URL, so avoid placing private account details in the scenario label.
- Use the written agreement when a lender, bank, school, or agency specifies a day-count convention.
- Do not use this result for amortizing loans, revolving credit, late fees, capitalized interest, or compounding investments.
- Treat withholding as a planning adjustment only. Tax rules, exemptions, and reporting rules are outside the calculation.
- Confirm currency, rounding, and payment timing before using the estimate in a contract or payoff request.
Worked Examples:
Eighteen-month deposit
A $10,000 principal at a 6.5% annual simple rate for 18 months has a year fraction of 1.5. Gross interest is $975.00, so the gross maturity amount is $10,975.00 before any withholding or product fees.
Forty-five-day quote
A $25,000 principal at 8.25% for 45 days on Actual / 365 produces about $254.28 of gross interest. On Actual / 360, the same principal, rate, and day count produces about $257.81 because the denominator is smaller.
Withholding check
If $975.00 of gross interest has 10% withholding applied, $97.50 is withheld and $877.50 remains as net interest. The net maturity amount is $10,877.50 because the principal is returned with interest after withholding.
FAQ:
Is simple interest the same as compound interest?
No. Simple interest applies the rate to the original principal. Compound interest adds earned interest back into the balance, so later interest can be calculated on a larger amount.
Why does Actual / 360 produce more interest than Actual / 365?
The same number of days is divided by 360 instead of 365. That creates a larger year fraction, which increases interest when principal and rate stay the same.
Does payout cadence change the final interest?
No. Payout cadence changes the checkpoint schedule and chart samples. It does not compound, reinvest, or subtract interim payouts from principal.
Can this estimate a loan payoff?
Only when the payoff is truly flat simple interest with no amortizing payments, late fees, capitalized interest, or changing principal. Most real payoff statements need lender-specific terms.
Glossary:
- Principal
- The original amount on which interest is calculated.
- Annual simple rate
- The yearly percentage applied to principal without compounding.
- Year fraction
- The term converted into part of a year for the simple-interest formula.
- Day-count basis
- The convention used to convert days, weeks, or some month assumptions into a year fraction.
- Gross maturity amount
- Principal plus gross interest before withholding.
- Net maturity amount
- Principal plus interest after the entered withholding percentage.
References:
- Consumer Financial Protection Bureau: simple interest rate and precomputed interest, for the distinction between interest on outstanding principal and precomputed interest.
- Bureau of the Fiscal Service: Simple Daily Interest, for a public simple daily interest example using a 360-day divisor.
- U.S. Department of the Treasury: Interest Rates FAQ, for official context on actual-day and 30 / 360 day-count treatment in Treasury yield material.