Simple Interest Calculator
Last updated: 21 August 2026
Reviewed by Gavin · Research and drafting assisted by AI
Simple Interest Calculator
Compute simple interest with the textbook formula I = P × r × t (interest equals principal × annual rate × years), the future amount A = P + I, and a side-by-side compound-interest comparison so you can see how the gap grows with rate and time. Presets cover $1k/$10k/$100k at 5 / 10 / 25 years. Edit any field; the result block updates live.
| Year | Interest accrued (I) | Total amount (A) |
|---|---|---|
| 1 | $50 | $1,050 |
| 2 | $100 | $1,100 |
| 3 | $150 | $1,150 |
Simple Interest Calculator
A simple interest calculator computes the interest earned (or charged) on a loan, savings account, or bond when interest is paid only on the original principal. The formula is one of the most widely taught relationships in personal finance and introductory accounting, I = P × r × t, where I is the interest accrued, P is the principal, r is the annual rate expressed as a decimal, and t is the term in years. The total amount owed or accumulated at the end of the period is then A = P + I. This free calculator handles all four variables, lets you solve for any one of them given the other three, and shows the compound-interest equivalent side by side so the gap between simple and compound growth is immediately visible.
Simple interest appears in real-world products that pay (or charge) interest on a flat basis without crediting interest on already-accumulated interest. Treasury bills, most short-term promissory notes, fixed-rate simple-interest loans, car loans that calculate interest on the original principal, some bridge financing, and many employee bonus or severance calculations are common examples. The OECD Glossary of Statistical Terms and the Federal Reserve consumer guides on interest both define simple interest as interest computed on the original principal only, with no interest-on-interest. When interest is added to the balance and itself earns interest in subsequent periods, the calculation switches to compound interest and the result grows faster than the simple-interest line.
How to Use This Calculator
- Enter the principal P, the starting amount in dollars. For a loan this is the amount borrowed; for a savings product it is the amount placed on deposit.
- Enter the annual interest rate r as a percentage (for example, 5 for 5%, or 7.25 for 7.25%). The calculator converts the percent to a decimal internally so the formula works as written in every textbook.
- Enter the term t in years. Fractional years are accepted: 0.5 represents six months, 0.25 a quarter, and 1/12 a month. For terms shorter than a year the simple-interest product P × r × t still applies directly.
- Pick a compounding frequency for the side-by-side comparison: annually, semi-annually, quarterly, monthly, or daily. This input does not affect the simple-interest result, it only shows what compound interest would have produced at the same nominal rate.
- Choose what to solve for, interest I, total amount A, principal P, rate r, or term t, and read the primary result block.
- Read the comparison strip and the year-by-year schedule below to see how the simple-interest total grows year over year and how it differs from the compound total.
The Formulae
The simple-interest identity is the linear relation
I = P × r × t
A = P + I = P × (1 + r × t)
For the comparison, the standard compound-interest identity is
A_compound = P × (1 + r / n) ^ (n × t)
I_compound = A_compound − P
where n is the number of compounding periods per year (1 = annual, 2 = semi-annual, 4 = quarterly, 12 = monthly, 365 = daily). The gap between the two results is
gap = A_compound − A_simple = P × [(1 + r / n)^(n·t) − (1 + r × t)]
and it is always non-negative for r > 0. As t increases or r increases, the gap widens roughly exponentially in t, which is why long-term savings products that compound beat simple-interest alternatives by such large margins over decades.
Solve-for-X rearrangements of I = P × r × t are elementary:
P = I / (r × t) (r and t must be > 0)
r = I / (P × t) (P and t must be > 0)
t = I / (P × r) (P and r must be > 0)
When the user picks one of these solve modes the principal field is repurposed as the target interest I, and the other two fields supply the known values. Each denominator must be strictly positive; the calculator reports ", " when a division would be undefined (for example, solving for rate when the term is zero).
Worked Examples
The table below uses the simple-interest identity I = P × r × t with r entered as a decimal (r = 5% = 0.05). The compound column uses monthly compounding (n = 12) at the same nominal rate for comparison.
| Principal (P) | Rate (r) | Term (t) | Simple I = P·r·t | Simple A = P+I | Compound A | Gap |
|---|---|---|---|---|---|---|
| $1,000 | 5.0% | 3 yr | $150.00 | $1,150.00 | $1,161.62 | $11.62 |
| $10,000 | 5.0% | 5 yr | $2,500.00 | $12,500.00 | $12,834.27 | $334.27 |
| $2,500 | 7.5% | 2 yr | $375.00 | $2,875.00 | $2,895.03 | $20.03 |
| $1,000 | 10.0% | 10 yr | $1,000.00 | $2,000.00 | $2,707.04 | $707.04 |
| $500 | 6.0% | 0.5 yr | $15.00 | $515.00 | $515.10 | $0.10 |
| $25,000 | 7.5% | 2 yr | $3,750.00 | $28,750.00 | $28,950.31 | $200.31 |
| $100,000 | 5.0% | 25 yr | $125,000.00 | $225,000.00 | $348,124.92 | $123,124.92 |
The first four rows illustrate the linear sensitivity: doubling the principal doubles the interest, tripling the rate triples the interest, and tripling the term triples the interest. The last row shows what happens at long horizons, at 5% over 25 years the simple-interest total is $225,000 while monthly compounding produces $348,125, a gap of more than $123,000 driven entirely by interest-on-interest.
Solve-for-X examples:
- Solve for rate: I want to earn $600 in interest on a $5,000 deposit over 3 years. r = I / (P × t) = 600 / (5,000 × 3) = 0.04 = 4%.
- Solve for term: I want $2,000 of interest on $10,000 at 5%. t = I / (P × r) = 2,000 / (10,000 × 0.05) = 4 years.
- Solve for principal: I want $1,500 of interest at 6% over 5 years. P = I / (r × t) = 1,500 / (0.06 × 5) = $5,000.
Where Simple Interest Shows Up
Simple interest appears in several places where the linear I = P × r × t formula is exactly what is written into the contract:
- Treasury bills (T-bills). US Treasury bills are short-term zero-coupon instruments quoted on a bank-discount basis that effectively pays simple interest on the face value for a term of 4, 8, 13, 26, or 52 weeks.
- Short-term promissory notes. Many small-business and personal loans under one year calculate interest as a flat percentage of the original principal with no amortization schedule.
- Some car-loan contracts. Older or non-amortizing auto-loan agreements quote a simple-interest rate and compute the interest charge as P × r × t on the original amount borrowed.
- Bridge loans and closing-cost financing. Real-estate bridge loans and seller-financed second mortgages often quote simple interest for terms under 24 months.
- Bonuses, severance, and back-pay awards. When an employer owes an employee a fixed additional amount tied to a period of service, the calculation is sometimes a simple-interest accrual.
- Education and textbook problems. The first interest calculation taught in personal-finance, accounting, and corporate-finance courses is the simple-interest identity, because the formula is linear and the algebra for solving for any variable is elementary.
Whenever a product quotes an APR but specifies that interest does not compound, the simple-interest formula is the right tool.
Common Mistakes
A handful of recurring errors come up when people use simple-interest formulas:
- Confusing the rate convention. Some products quote APR (annual percentage rate) while others quote APY (annual percentage yield, which already includes intra-year compounding). Simple-interest math always uses the nominal APR as a decimal; converting an APY to APR before plugging into I = P × r × t is a frequent source of error.
- Mixing decimal and percent inputs. Entering 5 when the formula expects 0.05 inflates the answer by a factor of 100. This calculator accepts the percent and divides by 100 internally; hand calculations should keep that convention consistent.
- Using compound math on a simple-interest contract. If the contract says simple interest, the right answer is the linear I = P × r × t. Accidentally computing (1 + r)^t and reporting it as the answer is wrong by an amount that grows with both rate and term.
- Forgetting partial-year terms. A six-month deposit has t = 0.5, not t = 6. A one-quarter deposit has t = 0.25. The linear formula scales correctly; entering integer months and ignoring the year conversion does not.
- Dividing by zero. Solving for principal requires r × t > 0; solving for rate requires P × t > 0; solving for term requires P × r > 0. A divide-by-zero is the most common reason solve-for-X calculations return ", " instead of a number.
Frequently Asked Questions
What is simple interest?
Simple interest is interest computed on the original principal only, with no interest-on-interest. For a principal P, an annual rate r (as a decimal), and a term t in years, the interest is I = P × r × t and the total amount is A = P + I. This is the standard definition used by the OECD Glossary of Statistical Terms, the Federal Reserve consumer guides on interest, and every introductory finance textbook (Brealey, Myers & Allen, Principles of Corporate Finance; Brooks, Financial Management: Core Concepts).
How does simple interest differ from compound interest?
Simple interest grows linearly in time: doubling t doubles the interest. Compound interest grows exponentially in time because each period's interest is added to the principal before the next period's interest is calculated. At the same nominal rate over a long term, compound interest always produces a larger total. The gap is small at low rates over short terms and large at higher rates over many years.
What products use simple interest?
US Treasury bills, many short-term promissory notes, some non-amortizing auto loans, bridge loans, certain bonus and severance calculations, and many introductory textbook examples. Simple-interest contracts are typically short-term because the linear growth leaves money on the table for long-horizon savers compared with compound-interest products.
Is a mortgage simple or compound interest?
Mortgages are amortizing loans that compound interest on the outstanding balance, not on the original principal. They are neither simple interest nor pure compound interest, they use compound interest with a declining balance. Use an amortization or mortgage calculator for that calculation; the simple-interest formula is the wrong tool.
Can this calculator solve for any of the four variables?
Yes. Pick "Solve for" in the controls, interest, total, principal, rate, or years, and the calculator returns the matching variable using the algebraic rearrangement of I = P × r × t. Each denominator must be strictly positive; otherwise the result is ", ".
How accurate is the calculator?
The arithmetic uses JavaScript IEEE-754 doubles, which carry about 15 significant decimal digits. For every realistic principal, rate, and term the result is exact to many more digits than you will ever need. Hand-verified test cases include $1,000 at 5% for 3 years giving I = $150.00 and A = $1,150.00 exactly.
Q: Can the Simple Interest Calculator, I = P × r × t with Compound Comparison be used for professional or commercial purposes? A: Yes, the Simple Interest Calculator, I = P × r × t with Compound Comparison provides mathematically correct results that are suitable for professional, commercial, and educational use. For the Simple Interest Calculator, I = P × r × t with Compound Comparison, For the Simple Interest Calculator, I = P × r × t with Compound Comparison, For high-stakes applications (medical, legal, financial), verify results with a domain expert. For the Simple Interest Calculator, I = P × r × t with Compound Comparison, the Simple Interest Calculator, I = P × r × t with Compound Comparison formulas used are well-established and validated against reference standards.
Q: How often are the Simple Interest Calculator, I = P × r × t with Compound Comparison formulas updated? A: the Simple Interest Calculator, I = P × r × t with Compound Comparison formulas are based on established scientific, mathematical, or industry-standard references and rarely require updates. When standards change (e.g., new physical constants, revised tax brackets, updated standards), the Simple Interest Calculator, I = P × r × t with Compound Comparison is updated to reflect the current authoritative source. For the Simple Interest Calculator, I = P × r × t with Compound Comparison, For the Simple Interest Calculator, I = P × r × t with Compound Comparison, Each calculator's references section lists the specific sources used.
References
- OECD, Glossary of Statistical Terms, "simple interest" entry (interest computed on the original principal only).
- Board of Governors of the Federal Reserve System, consumer guides on interest and credit (Federal Reserve Education).
- Brealey, R. A., Myers, S. C., and Allen, F., Principles of Corporate Finance, McGraw-Hill (standard reference for the I = P × r × t and A = P × (1 + r/n)^(n·t) identities).
- Brooks, R., Financial Management: Core Concepts, Pearson (introductory treatment of simple versus compound interest).
- US Treasury, Bureau of the Fiscal Service, Treasury bill pricing methodology (bank-discount basis equivalent to simple interest on face value).
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