What simple interest is
Simple interest is charged on the original amount only. Whatever interest builds up sits to one side and never earns anything itself, so the amount added each period is the same from the first period to the last and the balance climbs in a straight line.
That is the whole idea, and it is what separates it from compound interest, where each period's interest joins the balance and starts earning in its own right. Over a few months the two are almost indistinguishable. Over decades they are not remotely the same thing.
You meet simple interest more often as a borrower than as a saver. Car loans, personal loans and United States federal student loans generally accrue it on the outstanding principal. Savings accounts and credit cards nearly always compound.
The formula, and the four ways to rearrange it
Everything on this page comes from one line:
Interest equals principal times rate times time. Add the interest to the principal and you get the end balance, which is the same relationship written as A = P(1 + rt).
Because there are four quantities and one equation, knowing any three finds the fourth. That is what the tabs above do:
- Balance — A = P(1 + rt). The everyday case: you know what you put in and want to know what comes out.
- Principal — P = A ÷ (1 + rt). Working backwards from a target, which is how you size a deposit.
- Term — t = (A ÷ P − 1) ÷ r. How long the money needs to sit there.
- Rate — r = (A ÷ P − 1) ÷ t. The rate a deal is really offering, which is useful when only the two amounts are quoted.
Getting the units right
This is where nearly every wrong answer comes from. The rate and the time have to be measured in the same period.
If the rate is annual, the time must be in years — eight months is 8 ÷ 12, or 0.667 years. If the rate is monthly, the time is in months and you use 8 directly. Mixing an annual rate with a count of months inflates the answer twelvefold, which is exactly the mistake the two dropdowns on this page exist to prevent.
Written with matching periods rather than years, the same formula is often given as I = Prn, where r is the rate for one period and n is the number of periods. It is the identical calculation under a different name.
Simple against compound, with the numbers
The difference is small at first and then it is not. Take $10,000 at 5%:
| After | Simple | Compounded yearly | Difference |
|---|---|---|---|
| 1 year | $10,500.00 | $10,500.00 | $0.00 |
| 5 years | $12,500.00 | $12,762.82 | $262.82 |
| 10 years | $15,000.00 | $16,288.95 | $1,288.95 |
| 20 years | $20,000.00 | $26,532.98 | $6,532.98 |
| 30 years | $25,000.00 | $43,219.42 | $18,219.42 |
After one year they are identical, because there has been nothing to compound yet. After thirty the compound balance is more than 70% higher. As a saver you want the right-hand column; as a borrower you want the left one.
What to put in each box
- Principal. The original amount borrowed or deposited, before any interest.
- End balance. Principal plus all the interest — the total repayable, or what the deposit is worth at the end.
- Interest rate. The quoted rate, with the dropdown set to the period it is quoted for. Most consumer rates are annual.
- Term. How long the money is committed, in years or months. Fractions are fine: half a year is 0.5, or 6 months.
The tab you choose decides which box disappears, because that is the one being worked out.
Where the method actually matters
Three cases where knowing which method applies changes a decision.
Paying a loan early. On a simple-interest loan, interest accrues on the outstanding principal, often daily. Paying a few days early genuinely reduces what you owe. On a precomputed-interest loan the total was fixed at signing and early payment saves nothing without a rebate clause, so it is worth checking which you have.
Comparing two quotes. A simple rate and a compound rate are not directly comparable. Over a one-year term they are close enough to ignore. Over five years or more, convert both to the same basis or compare the total repayable instead.
Reinvesting a coupon. A bond pays simple interest on its face value. If you spend the coupons your return is simple; if you reinvest them at a similar rate your return compounds. The instrument is the same, and the decision is yours.
What this calculator does not cover
- Compounding. Nothing here rolls interest back into the balance. For that, use a compound interest calculator.
- Repayments during the term. The principal is assumed to sit unchanged until the end. A loan you pay down monthly has a falling balance, and the interest falls with it.
- Fees and charges. Arrangement fees, late fees and insurance are outside the formula and can dwarf the interest on a short loan.
- Day-count conventions. Lenders differ on whether a year is 360 or 365 days, which moves short-term figures by a fraction of a percent.
- Tax and inflation. Interest earned is usually taxable, and a nominal gain is not a real one once prices have risen.
Frequently asked questions
What is the formula for simple interest?
I = Prt. Interest equals the principal multiplied by the rate multiplied by the time, with the rate and the time measured in the same period. Add the interest back to get the end balance, which gives the other form you will see written as A = P(1 + rt). $18,500 at 4.5% a year for six years earns $4,995 of interest and finishes at $23,495.
How do I calculate simple interest for months?
Keep the rate and the time in matching units. If the rate is annual and the term is in months, divide the months by twelve: $10,000 at 6% a year for eight months is 10,000 x 0.06 x (8 / 12) = $400. If instead you have a monthly rate, use the number of months directly: 0.5% a month for eight months is 10,000 x 0.005 x 8 = the same $400. The unit dropdowns above do this conversion for you.
What is the difference between simple and compound interest?
Simple interest is charged on the original principal only, so the amount added is identical every period and the balance rises in a straight line. Compound interest adds each period's interest to the balance, so the next period earns on a larger base and the line curves upward. $10,000 at 5% for five years earns $2,500 simple, or $2,762.82 compounded annually. Over thirty years the same comparison is $15,000 against $33,219.42.
How do I find the interest rate from a principal and a balance?
Rearrange the formula to r = (A / P - 1) / t. Divide the end balance by the principal, subtract one to get the total return, then divide by the number of years. Turning $20,000 into $30,000 over ten years is (1.5 - 1) / 10 = 5% a year. The Rate tab above does this and converts a monthly answer to an annual one.
How long does it take to reach a target balance?
Rearrange again to t = (A / P - 1) / r. To get from $20,000 to $30,000 at 3% simple interest a year takes (1.5 - 1) / 0.03 = 16.67 years. Note how slow that is compared with compounding, which would reach the same target in about 13.7 years at the same rate. That gap is the whole argument for compound growth.
Do banks use simple or compound interest?
Savings accounts, checking accounts and credit cards in the United States almost always compound, usually daily or monthly. Simple interest is more common on the borrowing side: most car loans, personal loans and federal student loans accrue simple interest on the outstanding principal. Bonds are a middle case, since the coupon itself is simple but you can compound it by reinvesting.
Is simple interest better for a borrower?
Yes, all else equal. With simple interest you never pay interest on interest, so a missed month does not start growing on itself the way a credit card balance does. Be careful about comparing on the method alone, though: a simple-interest loan at 14% still costs far more than a compound loan at 6%. Look at the rate and the total repayable, not just the label.
Can simple interest be calculated daily?
Yes, and it commonly is. Federal student loans in the United States accrue daily simple interest, calculated as the principal multiplied by the annual rate divided by 365, then multiplied by the days elapsed. The result over a full year matches the annual formula, but daily accrual is why paying a few days early reduces what you owe, and why a late payment costs a little more.
This is an educational calculation, not financial advice. It assumes the principal stays untouched for the whole term, that nothing compounds, and that no fees or charges apply. Lenders differ on whether a year counts as 360 or 365 days, which moves short-term figures slightly, and interest earned is usually taxable. Check the agreement for whether your interest is simple or compound before comparing two quotes. More about how we build and check these tools is on our About page, and our Privacy Policy explains what we do and do not collect — nothing you type here leaves your browser.