When you borrow money, you’re expected to pay for the use of it — and when you lend or deposit money, you expect to be paid for it. That payment is called interest. The simplest way to calculate it is, fittingly, called simple interest: a flat charge based only on the original amount, the rate, and how long the money is borrowed or invested.
Simple interest shows up on short-term loans, some car loans, and many basic finance problems. Understanding it is also the foundation for understanding compound interest, where the math builds on itself. This guide covers the formula, several worked examples, and the key rules for counting time.
The Three Components of Simple Interest
Every simple interest calculation has three ingredients:
- Principal (P): the original amount of money borrowed or invested.
- Interest rate (r): the percentage charged per year, written as a decimal (10% becomes 0.10).
- Time (t): how long the money is borrowed or invested, expressed in years or a fraction of a year.
The Simple Interest Formula
Simple interest is calculated with one short formula:
I = P × r × t
Where I is the interest, P is the principal, r is the annual interest rate (as a decimal), and t is the time in years. Because the interest is always based on the original principal — never on interest already earned — the calculation stays “simple.”
Worked Example: A Car Loan
Alan borrows $10,000 from the bank to buy a car. He agrees to repay it in 8 months, plus simple interest at 10% per year. How much interest does he owe?
Here, P = $10,000, r = 0.10, and t = 8/12 (8 months out of 12). Applying the formula:
I = $10,000 × 0.10 × (8/12) = $667
So Alan repays $10,000 in principal plus about $667 in interest. Notice what happens if he takes longer to repay. If he repays over 15 months instead, only the time changes:
I = $10,000 × 0.10 × (15/12) = $1,250
More time means more interest — the longer the money is outstanding, the more it costs.
Counting Time in Days: The Banker’s Rule
In real finance, time is often measured in days rather than tidy months. There are two common ways to count the days of a loan:
- Exact time: the precise number of days between two dates.
- Approximate time: assumes every month has 30 days.
The banker’s rule, widely used in the United States, combines exact time (the actual number of days) with ordinary interest (a 360-day year). Here’s an example.
An investment of $5,000 is made on August 31 and repaid on December 31 at 9% interest. The exact number of days between those dates is 106. Applying the banker’s rule:
I = $5,000 × 0.09 × (106/360) = $132.50
Finding the Maturity Value
The maturity value is the total amount due at the end — principal plus interest:
S = P (1 + rt)
Using the same $5,000 investment above:
S = $5,000 × [1 + 0.09 × (106/360)] = $5,000 × 1.0265 = $5,132.50
That matches the principal of $5,000 plus the $132.50 of interest we calculated — a useful way to check your work.
Rearranging the Formula
Because I = Prt has four variables, you can solve for any one of them if you know the other three. The same example ($5,000 at 9% earning $132.50) demonstrates each:
- Find time: t = I ÷ (P × r) = $132.50 ÷ ($5,000 × 0.09) = 0.2944 years, which × 360 = 106 days.
- Find the rate: r = I ÷ (P × t) = $132.50 ÷ ($5,000 × 106/360) = 0.09, or 9%.
- Find the principal: P = I ÷ (r × t), useful when you know the interest charged and want to back out the original amount.
Simple Interest vs. Compound Interest
The key difference is what the interest is calculated on. Simple interest is always based on the original principal — it never changes from period to period. Compound interest is calculated on the principal plus any interest already accumulated, so it grows faster over time.
On a one-year loan the difference is small, but over many years compounding pulls far ahead. That’s why simple interest is common on short-term loans, while savings accounts, credit cards, and long-term investments almost always use compound interest. If you’re saving, compounding works in your favor; if you’re borrowing, it works against you.
Frequently Asked Questions
Where is simple interest actually used?
Simple interest is common on short-term personal loans, many auto loans, some bonds, and certain promissory notes. It’s also the standard model for basic finance and math problems because it’s easy to calculate and understand.
Why do some calculations use 360 days instead of 365?
A 360-day year (“ordinary interest”) is a banking convention that predates calculators and makes the math cleaner. Using exact days over 360 — the banker’s rule — slightly increases the interest compared to a 365-day year, which is why it became the U.S. standard.
Does paying a simple-interest loan off early save money?
Yes. Because interest accrues based on time, repaying a true simple-interest loan sooner reduces the total interest you pay. (Always confirm your loan doesn’t carry a prepayment penalty.)
The Bottom Line
Simple interest comes down to one formula — I = Prt — built from principal, rate, and time. It’s charged only on the original amount, which keeps the math predictable and makes it ideal for short-term loans. Once you’re comfortable with simple interest, compound interest is the natural next step, since it applies the same idea repeatedly over time.