Simple Interest Calculator
Calculate simple interest on a principal amount.
Shows why compound interest grows faster over time.
I = Interest, P = Principal
r = Annual Rate, t = Time (years)
What Is Simple Interest?
Simple interest is the most basic way to calculate interest: a flat percentage of the original principal, per year, for the duration of the loan or investment. Interest never earns interest — that's the definition of "simple." A $1,000 loan at 5% for 3 years earns exactly $50 × 3 = $150 of interest, no more and no less.
Simple interest is most common on short-term consumer lending. US auto loans, most personal installment loans, bills of exchange, promissory notes, and Treasury bills are all simple-interest instruments. Mortgages, credit cards, and savings accounts use compound interest because they involve long time horizons where the "interest on interest" effect matters.
Because the math is linear, simple-interest calculations are what textbooks use to introduce the time value of money. It's also the right mental model for any short-term transaction — a 90-day note, a 6-month CD, an invoice paid late.
The Simple Interest Formula
I— interest (dollars)P— principal (initial amount borrowed or invested)r— annual interest rate, as a decimal (5% → 0.05)t— time in years (6 months → 0.5, 90 days → 90/365)A— total amount (principal + interest) at maturity
Rearranging the formula lets you solve for any one of the four variables:
- Solve for rate:
r = I ÷ (P × t) - Solve for time:
t = I ÷ (P × r) - Solve for principal:
P = I ÷ (r × t)
Worked Example — Derek Borrows $100
Simple vs Compound — A Numeric Contrast
The difference between simple and compound interest is trivial over 1 year and enormous over 30. Here is $10,000 at 6%:
| Years | Simple Interest Balance | Compound Interest Balance | Difference |
|---|---|---|---|
| 1 | $10,600 | $10,600 | $0 |
| 5 | $13,000 | $13,382 | +$382 |
| 10 | $16,000 | $17,908 | +$1,908 |
| 15 | $19,000 | $23,966 | +$4,966 |
| 20 | $22,000 | $32,071 | +$10,071 |
| 30 | $28,000 | $57,435 | +$29,435 |
At year 1 the two are identical. By year 30, compound interest produces more than double the simple balance. This is why borrowers prefer simple interest (less total interest paid) and savers prefer compound (more growth).
Day-Count Conventions — 360 vs 365
When simple interest is calculated in days, the "day-count convention" determines what number you divide by. The two standards in US lending:
- Exact interest (365-day year): Used by most US consumer lenders and on this calculator when you pick the "Days" time unit.
- Ordinary interest (360-day year, 12 × 30-day months): Used in commercial banking, money-market instruments, Treasury bills, and some commercial paper. Survives from pre-calculator days when 360 was easier to divide.
The same stated rate produces slightly more interest under the 360-day convention because the daily rate is higher: 6% ÷ 360 = 0.01667%/day vs 6% ÷ 365 = 0.01644%/day. Over 90 days on $10,000, that's $150.00 vs $147.95 — small per loan, meaningful across a bank's whole portfolio.
Rules of Thumb
On a chart, simple-interest balance is a straight line; compound-interest balance curves upward. Over 1–2 years they're visually identical. Over 20+ years the compound curve pulls away dramatically. Time is the lever that separates them.
If you're borrowing, a simple-interest loan at the same stated rate costs you less than a compound-interest loan. If you're saving, compound grows faster. That's why banks advertise APY (compound) on deposits and APR (often simple or near-simple) on loans.
For short-term (under 1-year) promissory notes or commercial paper, confirm whether interest is 360 or 365. The rate looks identical on paper but the 360-day convention adds about 1.4% to the final interest owed.
How to Use This Calculator
- Enter the principal — the original loan or deposit amount.
- Enter the annual interest rate as a percentage (e.g., 5 for 5%).
- Enter the time and choose a unit (years, months, or days). The calculator converts months and days into a decimal year automatically.
- Read the result panel — interest earned, total amount, and daily interest accrual.
- Compare to the chart showing the same inputs under simple vs compound interest. Extend the period to see the gap widen.
- Try rearranging — if you know the interest and want the rate, solve
r = I ÷ (P × t)manually or iterate on the rate slider until the interest matches.
Methodology & Assumptions
- Applies the textbook formula
I = P × r × twith no compounding or amortization. - Days are converted using a 365-day year (exact interest). Months use 12 months = 1 year.
- Daily interest output is principal × rate ÷ 365.
- The simple-vs-compound chart assumes annual compounding for the compound series, for visual clarity; in practice most compound instruments use monthly or daily compounding.
- Does not model fees, taxes, or payment schedules. For auto-loan amortization with simple interest, use our Amortization or Loan calculator.
- All math runs in your browser; no data leaves your device.
Glossary
- Principal
- The original amount borrowed or invested. In the formula,
P. - Rate
- The annual percentage applied to the principal. Convert percent to decimal before plugging in (5% → 0.05).
- Term
- The length of the loan or investment in years, months, or days. In the formula,
t. - Interest
- The cost of borrowing or the return on lending, expressed in dollars. In simple-interest math,
I = P × r × t. - Maturity value
- Total amount paid back at the end of the term.
A = P + I = P(1 + rt). - Ordinary interest
- Day-count convention using a 360-day year (12 × 30 days). Common in banking and money markets.
- Exact interest
- Day-count convention using a 365-day year. Standard on most US consumer loans.
- Promissory note
- A written promise to repay a specified sum. Often uses simple interest, particularly on short-term notes.
- Accrued interest
- Interest earned but not yet paid as of a specific date. For a simple-interest loan, accrued = P × r × (days elapsed ÷ 365).
- APR (Annual Percentage Rate)
- The nominal annual interest rate used in consumer-lending disclosures. For simple-interest loans, APR = the rate in the formula.
Frequently Asked Questions
The formula is I = P × r × t, where I is the interest, P is principal, r is annual rate (decimal), and t is time in years. The total amount is A = P + I = P(1 + rt). Example: $1,000 at 5% for 3 years → I = 1,000 × 0.05 × 3 = $150.
Simple interest is calculated only on the original principal — interest never earns interest. Compound interest is calculated on principal plus accumulated interest. Over 1 year at 5%, $1,000 gives $50 either way. Over 30 years, $2,500 simple vs $4,322 compound — a 73% gap.
On short-term consumer lending: US auto loans, personal installment loans, promissory notes, and Treasury bills. Mortgages and credit cards use compound interest. Note: "simple-interest auto loans" still amortize monthly — the "simple" refers to how interest accrues, not to the payment schedule.
Most US auto loans are simple-interest amortized loans. Interest accrues daily on the outstanding principal using a 365-day year. Each monthly payment covers interest first, then reduces the principal. Paying extra directly reduces principal, lowering future interest.
Convert time to a decimal fraction of a year. Months: t = months ÷ 12 (9 months → 0.75). Days: t = days ÷ 365 (exact) or days ÷ 360 (ordinary). On $10,000 at 6% for 90 days: exact = $147.95; ordinary = $150.00.
Use I = P × r × (days ÷ day-count). Day-count is typically 365 (exact interest, used by most consumer lenders) or 360 (ordinary interest, used in banking and money markets). The 360-day convention produces slightly more interest — about 1.4% more for the same stated rate.
US mortgages use compound interest, typically compounded monthly. Each payment splits between interest on the current balance and principal reduction. Canadian mortgages compound semi-annually by law, which is slightly friendlier to borrowers.
Ordinary interest uses a 360-day year (12 × 30-day months); exact interest uses 365. Ordinary gives about 1.4% more interest at the same stated rate. Bankers used the 360-day year because it was easier for mental math; it survives on commercial paper, T-bills, and some short-term notes.
For simple-interest math, APR is used directly. If APR is 8%, plug r = 0.08 into I = Prt. (Compound interest requires converting APR to a periodic rate.) Note that consumer APR in US disclosures includes finance charges beyond pure interest, so it's usually slightly higher than the note rate.
Yes — at the same rate and term, simple interest always costs the borrower less. $10,000 at 6% for 10 years: $6,000 simple vs $7,908 compound, a $1,908 difference. For savers, compound wins. That's why loans trend toward simple and savings accounts trend toward compound.