How it works
I = P × r × t A = P + I = P(1 + r t)
Here P is the principal, r is the annual interest rate as a decimal (5% = 0.05) and t is the time in years. Months are converted as t = months ÷ 12, and days as t = days ÷ 365. Some lenders use a 360-day year, the “banker's rule,” which produces slightly more interest.
The calculator also shows what the same principal would grow to with annual compounding, A = P(1 + r)t, so you can see how much interest-on-interest adds.
Rearranging the formula
- Rate: r = I ÷ (P × t)
- Time: t = I ÷ (P × r)
- Principal: P = I ÷ (r × t)
Worked examples
$10,000 at 5% for 3 years
I = 10,000 × 0.05 × 3 = $1,500.00. Total: $11,500.00. Compounded annually it would be $11,576.25.
$2,500 at 8% for 9 months
t = 9 ÷ 12 = 0.75 years. I = 2,500 × 0.08 × 0.75 = $150.00. Total: $2,650.00.
Solving for the rate
If $4,000.00 earns $360.00 of simple interest in 2 years, then r = 360 ÷ (4,000 × 2) = 4.5% per year.
Simple vs. compound interest
With simple interest the balance grows by the same dollar amount every year: a straight line. With compound interest each year's interest is added to the balance and earns interest itself, so growth speeds up over time. Over short periods the difference is small. $10,000.00 at 5% for 3 years earns $1,500.00 simple vs. $1,576.25 compounded annually. Over long periods it is huge: after 20 years the balance is $20,000.00 with simple interest vs. $26,532.98 compounded annually. For long-term savings, see the compound interest calculator.
Where simple interest is used
- Auto loans and many personal loans use simple interest that accrues daily on the outstanding principal. Paying early or extra reduces interest because the principal falls sooner.
- Student loans (federal) accrue simple daily interest. Interest that goes unpaid may later be capitalized.
- Short-term loans, notes and some bonds pay simple interest. Treasury bills and some CDs quote simple or discount yields for terms under a year.
- Mortgages charge interest monthly on the remaining balance, which is simple interest on a declining balance, but the payment schedule follows the amortization formula.
Simple interest on amortizing loans
A loan can accrue simple interest and still have a level monthly payment. Each month, interest is calculated on the current balance only. The rest of the payment reduces principal, so the next month's interest is smaller. The total interest you pay over the life of such a loan is less than P × r × t on the original amount, because the balance shrinks. For a payment schedule, use the loan calculator or amortization calculator.
Watch for add-on interest
Some short-term consumer loans calculate interest as P × r × t on the original amount and add it to the loan up front, even though you repay the principal over time. This “add-on” method makes the true annual cost much higher than the quoted rate. Always compare loans by their APR, which federal law requires lenders to disclose. Our APR calculator shows how fees raise the effective rate.
Daily interest
To find interest per day, divide the annual interest by 365: daily interest = P × r ÷ 365. For $10,000.00 at 5%, that is $1.37 a day. Lenders often quote this “per diem” figure for payoff amounts.
How simple interest is quoted in the real world
Exact vs. ordinary interest. “Exact” interest uses a 365-day year, while “ordinary” or banker's interest uses 360 days. On $10,000.00 at 6% for 90 days, exact interest is $147.95 and ordinary interest is $150.00. The difference is small on one loan but adds up on large commercial balances, so check the day-count convention in your loan documents.
Daily accrual and payment timing. On a daily simple-interest loan, interest accrues every day on the current principal. Paying a few days early means slightly less interest accrues before your payment, so more of it goes to principal. Paying late means more of your payment goes to interest. Over the life of an auto loan, consistently paying early can save a noticeable amount.
Savings accounts. Most savings accounts and CDs compound interest, typically daily or monthly. They quote an APY that includes compounding. Simple interest is more common on loans, bonds and short-term notes. If you are comparing a savings rate, use APY, and see the CD calculator for compounding.
A quick check on your answer
Simple interest grows in a straight line, so you can sanity-check results easily. Interest for one year is principal × rate. For two years it is exactly double, for six months exactly half. If a lender's quote doesn't scale this way, the loan is probably compounding, charging fees or using an add-on method. Ask for the APR.
Simple interest and inflation
If an investment pays simple interest at a rate lower than inflation, your money loses purchasing power even as the dollar balance rises. A 3% simple return during 4% inflation means your real return is negative. Compare your rate with the inflation calculator before locking money into a long-term, low-rate note.
In short, simple interest is easy to calculate and predictable, which is why it is used so widely for loans and short-term notes. Compounding matters more for long-term savings.
To compare a simple-interest offer with a compounding one, convert both to an annual effective rate, or simply run both calculators over the same period and compare the ending balances.
Frequently asked questions
What is the simple interest formula?
I = P × r × t, where P is principal, r is the annual rate as a decimal and t is time in years. The total amount is P + I.
How do I calculate simple interest for months or days?
Convert time to years: months ÷ 12, or days ÷ 365 (some lenders use 360). Then apply I = P × r × t.
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus interest already earned, so it grows faster over time.
Do car loans use simple interest?
Most U.S. auto loans use simple interest calculated daily on the outstanding balance, so paying early or paying extra reduces the total interest.
Is simple interest better for borrowers?
Generally yes, compared with compound interest at the same rate, because interest does not accrue on interest. But compare loans by APR, which includes fees.
How much simple interest is earned per day?
Daily interest = principal × annual rate ÷ 365. For $10,000 at 5%, that is about $1.37 a day.
What is the difference between exact and ordinary simple interest?
Exact interest divides the annual rate by 365 days; ordinary (banker's) interest divides by 360, which produces slightly more interest for the same number of days. Check your loan agreement for the day-count convention.