Article — Simple Interest Calculator
Simple interest calculator: the I = P r t formula explained
Simple interest is calculated only on the original principal of a loan or deposit using the formula I = P x r x t. A $10,000 deposit at 5% annual rate for 3 years earns $1,500 in simple interest, for a total of $11,500. Simple interest grows linearly: double the time, double the interest. Most consumer products (credit cards, mortgages, savings accounts) use compound interest, but US Treasury bills, most auto loans, family loans at the IRS Applicable Federal Rate, and short-term promissory notes use simple interest.
The calculator above accepts time in years, months, or days, converts internally to years, and applies I = P r t with the entered rate. It also computes the monthly-compounded equivalent for comparison so you can see how much the compounding assumption changes the answer.
What is simple interest?
Simple interest is the simplest model of interest accrual: a fixed percent of the original principal accrues each year, multiplied by the number of years the principal sits in the loan or deposit. No interest accrues on previously earned interest. A $1,000 loan at 6% simple interest accrues exactly $60 each year, every year, until paid off.
The concept dates to ancient lending practice and was formalized in medieval European banking. Modern US lending law (the Truth in Lending Act of 1968) requires lenders to disclose whether a loan uses simple or compound interest in the standard APR disclosure box. Most US auto loans are simple interest by statute or industry convention.
The US Treasury issues T-bills using a discount-yield convention that is closely related to simple interest. A 26-week T-bill with a 5% discount yield sells for $9,754 and pays $10,000 at maturity (182 days later). The $246 difference is the simple-interest equivalent of approximately 5.06% annualized, calculated on a 365-day year basis.
The simple interest formula
One equation drives every simple interest calculation. Rearrangements solve for any single unknown.
I = P × r × tA = P (1 + r t)P = I ÷ (r × t)r = I ÷ (P × t)t = I ÷ (P × r)Rate r must be entered as a decimal in the equations (5% becomes 0.05). Time t is in years (6 months becomes 0.5; 90 days becomes 0.247). The calculator handles both conversions automatically when you select a time unit and enter a percent rate.
Simple interest vs compound interest
Simple interest grows linearly; compound interest grows exponentially. The two are nearly identical for periods under one year. Over decades the gap is large. $10,000 at 5% for 30 years earns $15,000 in simple interest. The same $10,000 at 5% annually compounded over 30 years earns $33,219 — more than double. Einstein never actually called compound interest the eighth wonder of the world (the quote is apocryphal), but the underlying math justifies the sentiment.
For borrowers, the choice is reversed: simple interest is friendlier. A 30-year simple-interest car loan would cost half as much in interest as a compound-interest loan at the same rate. Auto lenders use simple interest in part because terms are short enough (typically 3 to 7 years) that the practical difference is modest, and the disclosure is cleaner under TILA rules.
Where simple interest is used
Simple interest dominates a narrow but important set of financial products. US Treasury bills (4, 8, 13, 17, 26, and 52 weeks) use simple-interest math under a discount-yield convention. Most US auto loans accrue interest daily as simple interest on the outstanding balance. Some personal loans and short-term promissory notes use simple interest. Family or private loans at the IRS Applicable Federal Rate (AFR) typically use simple interest to avoid imputed-income tax complications.
Compound interest dominates the rest of consumer finance: credit cards (typically daily compounding), savings accounts (typically monthly compounding), CDs, mortgages, student loans, and most investment products. When in doubt, check the disclosure box on the loan or deposit agreement.
How to solve for rate, principal, or time
The same five variables (I, P, r, t, A) interlock through one equation. Most exam and textbook problems give three values and ask for one. The trick is plugging in correctly and isolating the unknown.
- Find interest = P x r x t (5,000 x 0.04 x 2 = $400)
- Find rate = I / (P x t) (400 / (5,000 x 2) = 0.04 = 4%)
- Find time = I / (P x r) (400 / (5,000 x 0.04) = 2 years)
- Find principal = I / (r x t) (400 / (0.04 x 2) = $5,000)
- Find total amount = P (1 + r t) (5,000 x 1.08 = $5,400)
- Find original from total = A / (1 + r t) (5,400 / 1.08 = $5,000)
Simple interest on Treasury bills
US Treasury bills are short-term debt obligations of the federal government with maturities of one year or less. They are sold at a discount to face value. A 26-week T-bill with face value $10,000 might sell at auction for $9,754. At maturity 182 days later, the Treasury pays $10,000. The $246 return is simple interest, equivalent to about 5.06% annualized on a 365-day year basis.
T-bills are the canonical example of simple interest in practice. They serve as the risk-free benchmark for short-term rates in finance theory. The Federal Reserve's H.15 statistical release publishes current T-bill auction rates daily. As of late 2024 and into 2025, the 3-month T-bill yielded between 4.2% and 4.5%, depending on Fed policy and market conditions.
When comparing a T-bill yield to a savings account APY, remember the savings account already includes compounding. A 4.5% T-bill (simple) and a 4.5% APY savings account (compounded) earn essentially the same dollar amount over a year. Past one year, the savings account pulls ahead.
Simple interest loan examples
Three worked examples covering common simple-interest products. An auto loan: $25,000 at 7% simple interest for 5 years pays $25,000 x 0.07 x 5 = $8,750 in total interest. Monthly payment math is more complex because each payment changes the outstanding balance, but the total interest figure caps what you would pay if the loan were never paid down. A family loan: $50,000 at the long-term AFR of 5% for 7 years (a balloon repayment) pays $50,000 x 0.05 x 7 = $17,500 in interest. A short-term bridge loan: $100,000 at 8% for 90 days pays $100,000 x 0.08 x (90/365) = $1,973 in interest.
Common simple interest mistakes
The most common mistake is using rate as a percent (5) rather than a decimal (0.05) in the formula, producing a 100x overstatement. The second most common is forgetting to convert time to years; 3 months is 0.25, not 3. The third is mixing simple and compound interest in the same comparison without flagging it. The fourth is using 360-day banker's year and 365-day calendar year interchangeably; on long-term loans the difference can be hundreds of dollars. The calculator above uses a 365-day year.