Simple Interest, Explained: The I = P × r × t Formula and When Loans Actually Use It

The first time I tried to charge a friend interest on a short loan, I almost reached for a compound interest formula out of habit. That would have been wrong, and slightly unfair to him. For a loan that lasts a few months, simple interest is the honest, auditable way to do the math. It charges interest on the money you actually borrowed, and nothing else.

This post walks through what simple interest is, the one formula you need, a worked example you can check by hand, and the real-world contracts that use it instead of compounding. You can follow along in the Simple Interest Calculator, which shows the worked formula under every result.

What simple interest means

Simple interest is charged only on the original principal, every single period. It never earns interest on interest already accrued.

Picture a $1,000 loan at 6% per year. With simple interest, year one earns exactly $60, and year two earns another $60, and year three earns another $60. The balance the interest is calculated from stays frozen at $1,000 the whole time. The interest does not snowball.

That single rule is the entire difference between simple and compound interest, and it has a clean formula behind it.

The formula: I = P × r × t

Here is the whole thing:

interest = principal × rate × time
I = P · r · t

P is the principal, the original amount borrowed or invested.
r is the annual interest rate, written as a decimal (6% becomes 0.06).
t is the time, measured in years.

That last point trips people up. If your term is in months or days, convert it to a fraction of a year first: 90 days is 90 ÷ 365 of a year, and 6 months is 6 ÷ 12. The calculator handles that conversion for you when you switch the time unit, but it helps to know what is happening underneath.

Once you have the interest, the total repayment is just the principal added back on:

total = principal + interest = P + (P · r · t)

A worked example you can check by hand

Say you invest $5,000 at 6% annual simple interest for 3 years.

P = 5000
r = 0.06
t = 3

I = 5000 × 0.06 × 3 = 900

The interest comes to $900. Add the principal back and the total is $5,900.

Notice how easy that is to verify line by line. 6% of $5,000 is $300 a year. Three years of $300 is $900. There is no hidden growth on the growth, which is exactly why simple interest is the default for figures that need to survive an audit or a dispute. A student, a borrower, or a small-claims judge can all retrace the arithmetic in their head.

When loans and bonds use simple interest

Plenty of everyday finance runs on simple interest, even though most people assume everything compounds.

Car loans and many personal loans in the US accrue simple interest daily on the outstanding principal. As you pay the balance down, the daily interest shrinks with it.
Treasury bills and short-term notes are quoted on a simple-interest, days-to-maturity basis. The interest you see is the interest you actually collect at maturity.
Bridge loans and promissory notes between individuals or businesses usually state a flat annual rate applied simply over the term.
Statutory late-payment penalties on overdue invoices are simple interest by design, because contractual and legal interest needs to be easy to compute and hard to argue with.

Worked example for that last one: a $2,000 invoice is 30 days overdue, and the contract specifies 18% annual simple interest on late payments. That is 2000 × 0.18 × (30 ÷ 365) ≈ $29.59. Defensible, transparent, and quick to add to a reminder.

The big exceptions go the other way. Mortgages and savings accounts almost always compound. So do credit cards and most deposit products. Before you reach for the simple interest formula, read the contract and confirm which method it actually names. Assuming a savings account is simple will quietly understate what you earn over the years.

Simple vs compound: the gap that matters

Over a single year, simple and compound interest barely differ. On a $1,000 balance at 6%, both produce about $60. The difference is rounding noise for anything under a year, which is why short-term instruments lean on the simpler method.

Stretch the term out, though, and the two diverge sharply. Compound interest earns 6% on $1,060 in year two, not $1,000, and that head start grows every period. Over a few decades, the compound total dwarfs the simple total on the same principal and rate.

This cuts both ways depending on which side of the table you sit on:

As a borrower, simple interest is your friend. You pay interest only on what you owe, never on interest you have already been charged. A loan contract that says "simple interest" is working in your favor.
As a saver, compounding is what you want. A product marketed as "simple interest" is quietly giving up the snowball you would get from compounding.

To see the spread for your own numbers, run them through the Compound Interest Calculator and compare the totals side by side. And if you are weighing two real loan offers with different rates and terms, the Loan Comparison tool lines them up so the cheaper one is obvious.

Solving for the missing piece

The formula rearranges cleanly, which is handy when you know the interest but not the rate or term:

P = I / (r · t)     solve for principal
r = I / (P · t)     solve for rate
t = I / (P · r)     solve for time

For instance, if a $5,000 investment earned $900 over 3 years and you want the rate: r = 900 ÷ (5000 × 3) = 0.06, or 6%. The only thing to watch is dividing by zero, so solving for a rate needs both a non-zero principal and a non-zero term.

The short version

Simple interest is principal × rate × time, full stop. It charges on the original amount only, it is trivial to verify, and it is the standard for car loans, T-bills, short-term notes, and late-payment penalties. Compounding wins over long horizons, so use simple interest for the short-term instruments that genuinely rely on it, and switch tools the moment a contract says "compound."

When in doubt, type your three known values into the Simple Interest Calculator, read the fourth, and let the worked formula confirm the arithmetic for you.

Made by Toolora · Updated 2026-06-13