Simple Interest Formula Explained: I = P x r x t

Simple interest is the most straightforward way to measure the cost of borrowing money or the reward for lending it. Whether you are sizing up a short term loan, a fixed deposit, or a car finance offer, knowing the formula lets you check the numbers yourself instead of trusting whatever a salesperson tells you. This guide breaks the formula down piece by piece, walks through real examples, and shows exactly where simple interest differs from compound interest.

What is the simple interest formula?

The core formula is short enough to memorize in seconds: I = P x r x t. Here I stands for the interest earned or owed. To get the full balance at the end, you add that interest back to your starting amount, which gives the total amount formula A = P(1 + rt).

• P (principal) is the original sum of money you deposit or borrow. It never changes over the life of a simple interest arrangement.
• r (rate) is the annual interest rate expressed as a decimal. A rate of 5 percent becomes 0.05, and 12 percent becomes 0.12.
• t (time) is the length of the loan or investment measured in years. Six months is 0.5, and 18 months is 1.5.
• I (interest) is the result: the extra money added on top of the principal.

The single most important idea is that simple interest is always calculated on the original principal alone. The interest earned in year one does not start earning its own interest in year two. That is the defining trait that separates it from compound interest, and it keeps the math clean and predictable.

A worked example, step by step

Suppose you deposit 2,000 dollars into an account paying 4 percent simple interest per year, and you leave it there for 3 years. Here is how to find the interest and the final balance.

1. Identify the principal: P = 2,000.
2. Convert the rate to a decimal: 4 percent becomes r = 0.04.
3. Set the time in years: t = 3.
4. Multiply them together: I = 2,000 x 0.04 x 3 = 240. So you earn 240 dollars in interest.
5. Add the interest to the principal for the total: A = 2,000 + 240 = 2,240 dollars.

Notice how each year added exactly 80 dollars (2,000 x 0.04), and three identical years gave 240 dollars. That even, repeating pattern is the signature of simple interest. If you ever want to skip the arithmetic, the simple interest calculator does all four steps instantly.

Simple interest reference table

The table below shows the interest earned on a 1,000 dollar principal at several common rates and time periods. Use it as a quick sanity check before committing to any deal.

Because simple interest scales in a straight line, you can read this table flexibly. At 5 percent over 3 years you earn 150 dollars on 1,000, so on 4,000 dollars you would earn four times that, or 600 dollars. The relationship is purely proportional.

Simple interest vs compound interest

The two methods agree for the very first period, then drift apart. With simple interest the base stays fixed at the original principal. With compound interest, each period's interest is added to the balance and then earns interest itself, so the balance accelerates over time.

Over 10 years the compound balance pulls roughly 594 dollars ahead, and the gap widens the longer you wait. For savers, compounding is the friendlier option, while for borrowers, simple interest is usually cheaper. To see the gap for your own numbers, read our guide on compound interest or try the compound interest calculator.

Where simple interest shows up in real life

• Car loans and personal loans in many regions quote simple interest, especially shorter term financing.
• Certificates of deposit and fixed deposits sometimes pay simple interest when the term is short.
• Bonds often pay simple interest in the form of fixed periodic coupons on the face value.
• Short term and bridge lending between businesses frequently uses simple interest for its transparency.
• Retail installment plans and some buy now pay later structures advertise a flat simple rate.

Understanding which method applies matters. The same headline rate can cost very different amounts depending on whether interest compounds. When a contract simply states a flat annual percentage with no mention of compounding, simple interest is usually the safe assumption, but always confirm.

How day-count conventions change the answer

When time is measured in days instead of whole years, lenders divide the day count by either 360 or 365. The 360 day method, known as ordinary interest or the banker's rule, produces slightly more interest than the 365 day exact interest method, so the convention you assume can shift the final figure. For short term instruments the difference is small but real, and it is worth knowing which one your contract uses.

Take a 1,000 dollar loan at 8 percent held for 90 days. Under exact interest you use t = 90 / 365, which gives about 0.2466 years and 19.73 dollars of interest. Under ordinary interest you use t = 90 / 360, which gives exactly 0.25 years and 20.00 dollars. Same principal, same rate, same number of days, yet the banker's rule quietly costs a borrower 27 cents more.

The gap looks tiny on a single small loan, but it scales with the principal and with how often the loan turns over. On large short term balances that roll many times a year, the choice between 360 and 365 days adds up. Unless a document says otherwise, treat the day count as a detail worth checking rather than an afterthought.

Common mistakes to avoid

• Forgetting to convert the rate to a decimal. Plugging in 5 instead of 0.05 inflates your answer by a hundred times. Always divide the percentage by 100 first.
• Using the wrong units for time. The rate is annual, so time must be in years. For 9 months, use 0.75, not 9.
• Mixing up interest and total amount. I = P x r x t gives only the interest. Remember to add the principal back if you want the final balance.
• Applying simple interest when the product actually compounds. This understates the cost of credit card balances and long term loans, which almost always compound.
• Rounding too early. Keep full precision through the calculation and round only the final figure to avoid drift.

If you work with percentages often, it helps to be comfortable converting between forms. Our explainer on percent change and the percentage calculator are handy companions for double checking rate conversions.

Rearranging the formula to solve for any variable

Because the formula is just multiplication, you can rearrange it to find whichever value is missing. This is useful when you know the interest you want and need to back out the rate or the time.

For example, if you earned 90 dollars of interest on a 1,500 dollar principal over 2 years, the rate was r = 90 / (1,500 x 2) = 0.03, or 3 percent. Each version of the formula answers a different practical question.

The simple interest formula rewards anyone willing to spend thirty seconds checking the numbers. Memorize I = P x r x t, keep your rate in decimal form and your time in years, and you will always know exactly what a flat rate loan or deposit is worth. When you need an answer fast, lean on the calculator above and let it handle the arithmetic for you.