Simple Interest Formula — I = PRT with Examples

The simple interest formula is $I = Prt$. It tells you how much interest is charged or earned when the interest is calculated only on the original principal, not on earlier interest.

If $P$ is the principal, $r$ is the rate as a decimal, and $t$ is the time, then

$$I = Prt$$

This gives the interest only. If you also want the total amount after interest, add the principal back:

$$A = P + I = P(1 + rt)$$

Use this model only when the problem says the interest is simple. If interest is added back into the balance and future interest is charged on that larger balance, that is compound interest instead.

What $I = Prt$ Means

$P$ is the principal, the original amount borrowed or invested.

$r$ is the interest rate written as a decimal. For example, $6\% = 0.06$.

$t$ is time. If $r$ is an annual rate, then $t$ must be in years.

That condition matters. If a problem gives $18$ months at an annual rate, use $t = 18/12 = 1.5$, not $t = 18$.

Why The Simple Interest Formula Works

With simple interest, the base never changes. Each period's interest is calculated from the same original principal, so the interest grows at a constant rate.

That is why the growth is linear. If you double the time, the interest doubles. If you halve the rate, the interest is halved.

Worked Example: $2{,}000$ At $4\%$ For $18$ Months

Suppose a loan has principal $P = 2000$, annual simple interest rate $r = 4\%$, and time $t = 18$ months.

First convert the rate to a decimal and the time to years:

$$r = 0.04,\quad t = \frac{18}{12} = 1.5$$

Now use the formula:

$$I = Prt = 2000(0.04)(1.5)$$ $$I = 80 \cdot 1.5 = 120$$

So the interest is $120$.

To find the total amount owed, add the principal:

$$A = 2000 + 120 = 2120$$

So after $18$ months, the simple interest is $120$ and the total amount is $2120$.

Common Simple Interest Mistakes

Using The Percent Instead Of The Decimal

In $I = Prt$, the rate must be a decimal. Using $4$ instead of $0.04$ makes the answer $100$ times too large.

Mixing Time Units

If the rate is yearly, time must be in years. If the rate is monthly, time should be in months. The units have to match.

Using The Formula For Compound Interest

Simple interest uses the original principal only. Compound interest uses a changing balance, so $I = Prt$ does not describe that situation.

When The Simple Interest Formula Is Used

Simple interest appears in introductory finance problems, some short-term loans, and situations where the agreement explicitly says interest is simple.

In many real savings accounts and loans, interest compounds. So before using $I = Prt$, check the condition instead of assuming.

Quick Setup Check

Before you finish, ask:

1. Is the rate written as a decimal?
2. Do the rate and time use matching units?
3. Does the problem actually say the interest is simple?

If those answers are yes, the setup is usually correct.

Try A Similar Problem

Try your own version with $P = 750$, $r = 8\%$ per year, and $t = 9$ months. Find the interest first, then the total amount. If you want a useful comparison, solve the same setup again with compound interest and notice why the answers differ.