Simple interest, fully explained: formula, worked examples and when it’s used

Simple interest is the oldest bargain in finance: lend or borrow a sum of money, and the interest is always worked out on that original sum — never on interest itself. One formula runs the entire arrangement, the simple interest formula, I = P × r × t, and in this article I will take it apart letter by letter, show exactly how to calculate simple interest on real dollar amounts, and work through simple interest examples from a bank deposit to a car loan. I will also set it beside compound interest on the same $10,000, because the year-by-year gap between the two is the clearest way I know to see what compounding is actually worth.

The simple interest formula, piece by piece

The formula has four letters, and each one is a question you can answer about any deal:

• P — the principal. The amount you start with: the deposit you make or the sum you borrow.
• r — the rate. The yearly interest rate written as a decimal, so 6% becomes 0.06 and 8% becomes 0.08.
• t — the time. How long the money is out, measured in years. Six months is t = 0.5; eighteen months is t = 1.5.
• I — the interest. The answer: the dollars the principal earns, or costs, over that time.

Multiply the first three and you get the fourth. Add the interest back onto the principal and you have the final amount, which is why you will also see the formula written as A = P × (1 + r × t). Two properties follow from the shape of this formula, and they explain everything else in this article. First, the rate and the time must share a clock — an annual rate needs the time in years. Second, simple interest grows in a straight line: the same number of dollars arrives every single year, because the base it is calculated on never moves.

How to calculate simple interest: a worked example

Say I deposit $5,000 at 6% simple interest and leave it for 4 years. The calculation has three moves:

1. Find one year of interest. $5,000 × 0.06 = $300. That is what the principal earns in a single year — $25 a month, if you want the monthly view.
2. Scale it by the time. Four years at $300 a year gives I = $300 × 4 = $1,200. Written in one line: I = 5,000 × 0.06 × 4 = $1,200.
3. Add it back. Final amount A = $5,000 + $1,200 = $6,200.

Part-years are where people hesitate, so here is a second, smaller example. Borrow $1,200 at 9% for 6 months. The time is 6 ÷ 12 = 0.5 years, so I = 1,200 × 0.09 × 0.5 = $54. Same formula, same three moves — the only adjustment is expressing the time in years before you multiply.

Simple interest examples: the same $10,000, simple vs compound

The straight line becomes obvious when you race it against compounding. Here is $10,000 at 8% for up to ten years, calculated both ways — simple interest on the left, compound interest (compounded once a year) on the right:

$10,000 at 8%. Simple interest adds a flat $800 every year; compound interest is recalculated each year on the growing balance. Every figure computed from the two formulas for this article.

Year one is a dead heat — $800 either way, because there is not yet any interest for compounding to work on. By year two the compound column is $64 ahead, and by year ten it is ahead by $3,589.25, having earned $11,589.25 against simple interest’s $8,000. Nothing about the rate or the principal changed; the compound column simply pays interest on interest, and the advantage compounds along with the money. If you want the right-hand column run on your own figures, our compound interest calculator does it with the compounding frequency of your choice.

Rearranging the formula: solve for the piece you are missing

Because the formula is one multiplication, it turns inside out cleanly. Given any three of the four letters, the fourth is a division away:

• Finding the rate. My $5,000 deposit came back as $5,800 after 4 years. The interest is $800, so r = 800 ÷ (5,000 × 4) = 0.04 — the account was paying 4%.
• Finding the time. How long does $2,000 at 5% need to earn $500? It earns $100 a year, so t = 500 ÷ (2,000 × 0.05) = 5 years.
• Finding the principal. I want $900 of interest at 6% over 3 years. P = 900 ÷ (0.06 × 3) = $5,000 — the same deposit from the worked example, seen from the other side: $5,000 earns $300 a year, and three years of that is exactly $900.

When simple interest is actually used

Simple interest survives wherever a deal is short, fixed and supposed to be easy to verify by hand. You will meet it in more places than you might expect:

• Simple-interest car loans. Most US auto loans accrue interest daily on the balance you still owe — simple interest with a daily clock — which is why paying early in the month genuinely costs less than paying late.
• Short-term promissory notes and private loans. A sum borrowed and repaid in one payment, with I = P × r × t written into the note.
• Federal student loans. While you are in school, interest accrues on the original principal only; it does not compound until a capitalization event adds it to the principal.
• Bond coupons. Each coupon payment is simple interest on the bond’s face value — the payments only start compounding if you reinvest them.

And where it is not used is just as telling: savings accounts, CDs and money market funds compound, and credit cards are their own daily-balance machine. The moment interest starts being charged or paid on earlier interest, you have left the straight line behind.

Sources: the simple and compound interest formulations follow standard finance-textbook definitions (I = P × r × t; A = P × (1 + r/n)^nt); consumer descriptions of simple-interest auto loans and federal student loan accrual follow Consumer Financial Protection Bureau (CFPB) and Federal Student Aid guidance. Every figure in this article was computed from those formulas for this article; rates are illustrative, not market quotes.