Simple Interest Calculator (I = P × r × t)
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.
Simple interest formula: **I = P × r × t** — where P is the principal, r is the annual rate as a decimal, and t is time in years. Example: $1,000 at 5% for 3 years → I = 1,000 × 0.05 × 3 = **$150**. The final amount is P + I = **$1,150**. Unlike compound interest, simple interest is always calculated on the original principal only.
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.
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.
How it works
2 min readSimple 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:
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 = $3002. 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.
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.