Math

Simple Interest Calculator (I = P × r × t)

Q: What is the simple interest formula?

The formula is **I = P × r × t**, where P is the principal, r is the annual rate as a decimal (e.g., 5% → 0.05), and t is the time in years. Final amount = P + I = **P × (1 + r × t)**. Example: $2,000 at 6% for 2 years → I = 2,000 × 0.06 × 2 = **$240**; final amount = $2,240.

Q: What's the difference between simple and compound interest?

In **simple interest**, interest is always computed on the **original principal** — it never grows. In **compound interest**, interest is added to the principal each period and earns interest itself. Over 10 years at 10%, compound yields ~30% more than simple. Use compound calculations for long-term investing.

Q: How do I convert an annual rate to monthly simple interest?

**Divide** the annual rate by 12: monthly rate = APR / 12. Example: APR 12% → 1% simple per month. So $1,000 for 3 months = 1,000 × 0.01 × 3 = $30. Note: this does NOT work for compound interest, which uses `(1 + APR)^(1/12) − 1`.

Q: When is simple interest actually used?

Mainly for: **late payment penalties** (contracts specify a daily or monthly punitive rate), **short-term personal loans** (under 12 months), **discount Treasury bills**, and some **private loan agreements**. Most mortgages, CDs, and savings accounts use compound interest.

Q: Can I use this calculator for late payment interest?

Yes. Enter the **overdue amount** as principal, the **contracted penalty rate** (annual), and the **number of days** late as time (select Days). The calculator converts days to years automatically: t = days / 365.

Q: What should I compare when choosing between loan offers?

Always compare by **APR (Annual Percentage Rate)**, which includes fees. The simple nominal rate can be misleading — two loans with the same rate but different origination fees can have very different real costs. Most countries require lenders to disclose APR.

Q: Does this calculator work with daily and monthly rates?

The calculator accepts an **annual rate** and a time in years, months, or days. If your contract specifies a monthly rate, convert it: monthly_rate × 12 = annual. Enter that in the annual rate field and choose 'Months' for time.

Q: Does the result include taxes on interest?

**No** — results are gross (pre-tax). Tax treatment varies by country. In the US, interest income is generally taxed at your ordinary income rate. Subtract 15–25% from interest earned depending on your bracket to estimate net return.

Calculate simple interest in seconds: enter principal, annual rate, and time (years, months, or days). Get total interest, final amount, and monthly/daily breakdowns. Includes worked example and simple vs. compound table.

Data verified · June 2026
Edited by Martín Rodríguez
Formula verified by automated tests
Private — runs on your device

Suggest an improvement

Calculator Free · Private

Edited by: Martín Rodríguez (editorial policy )

Suggest an improvement

🧮 Keep calculating

Compound Interest CalculatorCalculate compound interest with monthly contributions. See end balance, total interest earned, and a year-by-year breakdown using the A=P(1+r/n)^(nt) formula.Fixed Deposit Net Annual ReturnsCalculate fixed deposit net returns after taxes. Free instant calculator for your savings.Loan Payment CalculatorCalculate your monthly loan payment, total interest and amortization schedule. Works for personal loans, auto loans and mortgages.Car Loan Interest Deduction Calculator (2026)Up to $10,000 of interest on a new, U.S.-assembled personal-use vehicle, with the $100k/$200k MAGI phase-out and your federal income tax savings.

Want to change something?Edit any field and calculate again.

Instant resultIt recalculates in your browser, no page reload.

Fast and transparent

How to use this calculator

Follow this tool’s steps, then review its formula, assumptions, and limits below.

Step by step

Enter the principalEnter the initial principal amount (e.g., $10,000).

Enter the annual rateEnter the annual interest rate as a percentage (e.g., 8%).

Enter the timeEnter the time value (e.g., 3) and select the unit: Years, Months, or Days.

Simple interest is the most basic way to calculate return or cost on capital: it's always applied to the original principal, never to accumulated interest. The formula is I = P × r × t (interest = principal × annual rate × time in years). It is used for late payment penalties, short-term personal loans, discount Treasury bills, and wherever there is no compounding. Enter your principal, annual rate, and time (years, months, or days) to get the total interest, final amount, and average monthly and daily interest. For investments with reinvested interest, use the compound interest calculator.

When to use this calculator

Calculating late payment interest on a bill, invoice, or rent.
Estimating the total cost of a 6-month or 12-month personal loan with a fixed rate.
Comparing simple vs. compound interest before choosing an investment.
Working out interest on a tax debt or penalty.
Drafting a private loan agreement and updating the amount to a specific date.

Day-Count Conventions for Simple Interest (and their effect)

How the day-count basis changes simple-interest results on the same loan.

Convention	Days in period	Days in year	Where it's used	$10,000 @ 6%, 90 days
Actual/365 (Fixed)	Actual	365	GBP loans, many retail/personal loans	$147.95
Actual/360	Actual	360	USD money markets, most US commercial loans	$150.00
30/360 (Bond Basis)	30 per month	360	US corporate & municipal bonds	$150.00
Actual/Actual (ISDA)	Actual	365 or 366	US Treasury notes & bonds	$147.95 (≈)
30E/360 (Eurobond)	30 per month	360	Eurobonds, European fixed income	$150.00

Simple interest = Principal × Rate × (Days in period ÷ Days in year). The convention changes only the time fraction, not the formula. Actual/360 yields MORE interest than Actual/365 for the same period because the denominator is smaller — a 360-day year charges ~1.39% more interest than a 365-day year. The last column shows total interest on $10,000 at a 6% annual rate held exactly 90 days. This calculator uses Actual/365 (days ÷ 365) for the Days option. Sources: ISDA 2006 Definitions; CFA Institute fixed-income curriculum; SIFMA day-count standards.

How it works

Simple Interest Formula

Simple interest is always computed on the original principal, not on accumulated interest:

I = P × r × t
Final amount = P × (1 + r × t)

Where:

I = total interest

P = initial principal

r = annual interest rate as decimal (8% → 0.08)

t = time in years

Quick Reference: Simple Interest on $1,000 at Different Rates & Terms

Principal	Rate	6 months	1 year	2 years	5 years
$1,000	3%	$15	$30	$60	$150
$1,000	5%	$25	$50	$100	$250
$1,000	8%	$40	$80	$160	$400
$1,000	10%	$50	$100	$200	$500
$1,000	15%	$75	$150	$300	$750
$5,000	5%	$125	$250	$500	$1,250
$10,000	5%	$250	$500	$1,000	$2,500

Converting Time Units

Rate given as	Time input	Convert to years
Annual (e.g., 10%)	Years	t = years
Annual (e.g., 10%)	Months	t = months / 12
Annual (e.g., 10%)	Days	t = days / 365
Monthly (e.g., 1%)	Months	t = months
Daily	Days	t = days

Important: always match the rate period to the time period before calculating.

Simple vs. Compound Interest — The Gap Over Time

Over short periods the difference is minimal. Long-term, compound interest dominates:

Period	Simple (10%/yr)	Compound (10%/yr)	Compound advantage
Start	$1,000	$1,000	—
1 year	$1,100	$1,100	0%
2 years	$1,200	$1,210	+0.8%
5 years	$1,500	$1,611	+7.4%
10 years	$2,000	$2,594	+29.7%
20 years	$3,000	$6,727	+124%
30 years	$4,000	$17,449	+336%

For long-term comparisons, always use compound interest.

Common Real-World Uses

1. Late Payment Penalties

Contracts often specify a daily or monthly simple rate. For a $5,000 debt 30 days late at 0.2% daily:

Interest = 5,000 × 0.002 × 30 = $300

2. Short-Term Personal Loans

Some lenders apply simple interest on 3–12 month loans. The real effective cost (APR) is always higher when fees are included.

3. Discount Treasury Bills

T-bills are priced below face value. The return is often quoted as a simple annualized rate.

APR vs. APY: Why They Differ

APR is the nominal rate without compounding — close to simple interest. APY includes compounding — what you actually earn or pay. With APR 12% and monthly compounding:

APY = (1 + 0.12/12)^12 − 1 ≈ 12.68%

For mortgages and credit cards, lenders are legally required to disclose APR; always check both.

Common Calculation Mistakes

1. Forgetting unit conversion: if the rate is annual and time is in months, divide t by 12.
2. Using 360 vs. 365 days: US business contracts often use a 360-day year for simplicity.
3. Confusing simple with compound: loans over 1 year are almost always compound, not simple.
4. Ignoring fees: the nominal rate alone understates the real cost of borrowing.

Example: $10,000 at 8% annual for 3 years

Principal (P): $10,000.

Annual rate (r): 8% → 0.08.

Time (t): 3 years.

Formula: I = P × r × t.

Calculation: 10,000 × 0.08 × 3 = $2,400 of interest.

Final amount: 10,000 + 2,400 = $12,400.

Avg monthly interest: 2,400 / 36 ≈ $67.

Avg daily interest: 2,400 / 1,095 ≈ $2.19.

With a simple annual rate of 8% on $10,000 over 3 years, you earn $2,400 in interest and end with $12,400. Under compound interest at the same rate, the final amount would be ~$12,597 — the gap grows substantially over longer periods.

Frequently asked questions

What is the simple interest formula?

The formula is I = P × r × t, where P is the principal, r is the annual rate as a decimal (e.g., 5% → 0.05), and t is the time in years. Final amount = P + I = P × (1 + r × t). Example: $2,000 at 6% for 2 years → I = 2,000 × 0.06 × 2 = $240; final amount = $2,240.

What's the difference between simple and compound interest?

In simple interest, interest is always computed on the original principal — it never grows. In compound interest, interest is added to the principal each period and earns interest itself. Over 10 years at 10%, compound yields ~30% more than simple. Use compound calculations for long-term investing.

How do I convert an annual rate to monthly simple interest?

Divide the annual rate by 12: monthly rate = APR / 12. Example: APR 12% → 1% simple per month. So $1,000 for 3 months = 1,000 × 0.01 × 3 = $30. Note: this does NOT work for compound interest, which uses (1 + APR)^(1/12) − 1.

When is simple interest actually used?

Mainly for: late payment penalties (contracts specify a daily or monthly punitive rate), short-term personal loans (under 12 months), discount Treasury bills, and some private loan agreements. Most mortgages, CDs, and savings accounts use compound interest.

Can I use this calculator for late payment interest?

Yes. Enter the overdue amount as principal, the contracted penalty rate (annual), and the number of days late as time (select Days). The calculator converts days to years automatically: t = days / 365.

What should I compare when choosing between loan offers?

Always compare by APR (Annual Percentage Rate), which includes fees. The simple nominal rate can be misleading — two loans with the same rate but different origination fees can have very different real costs. Most countries require lenders to disclose APR.

Does this calculator work with daily and monthly rates?

The calculator accepts an annual rate and a time in years, months, or days. If your contract specifies a monthly rate, convert it: monthly_rate × 12 = annual. Enter that in the annual rate field and choose 'Months' for time.

Does the result include taxes on interest?

No — results are gross (pre-tax). Tax treatment varies by country. In the US, interest income is generally taxed at your ordinary income rate. Subtract 15–25% from interest earned depending on your bracket to estimate net return.

Sources & references

Methodology & trust

Editorial

Math calculator with its formula verified automatically against Investopedia — Simple Interest, per our editorial policy and methodology.

Updates

Updated: June 2026. Parameters are verified periodically against the cited sources.

Privacy

Calculations run 100% in your browser. We do not store or transmit your data.

Limitations

Indicative results. For critical decisions, consult a professional.

📌 How to cite this calculator

APA format

Rodríguez, M. (2026). Simple Interest Calculator (I = P × r × t). Hacé Cuentas. https://hacecuentas.com/en/simple-interest-calculator

BibTeX

@misc{hacecuentas_simple_interest_calculator_2026,
  author       = {Rodríguez, Martín},
  title        = {{Simple Interest Calculator (I = P × r × t)}},
  year         = {2026},
  howpublished = {\url{https://hacecuentas.com/en/simple-interest-calculator}},
  note         = {Hacé Cuentas}
}

Content licensed under CC-BY 4.0 — reuse it citing the source with a link to Hacé Cuentas.

✉️ Report an error in this calculator