Calculate simple interest

Simple interest is calculated as $I=Prt$ , where $P$ is the principal, $r$ the annual interest rate expressed as a decimal, and $t$ the time in years; the accumulated amount is $A=P+I=P(1+rt)$ . The learner interprets interest as proportional to principal, rate, and time, converts time units consistently, and distinguishes linear simple interest from compound interest, including solving for an unknown quantity in routine contexts.

Detailed Explanation: Calculate simple interest

Simple interest is calculated only on the original amount of money, called the principal.

Use the formulas

I=Prt

and

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

where:

$P$ is the principal,
$r$ is the annual interest rate written as a decimal,
$t$ is the time in years,
$I$ is the interest earned,
$A$ is the accumulated amount, or final balance.

Example

A student deposits 1{,}200 $in an account earning$ 5% $simple interest per year for$ 2.5$ years. Find the interest earned and the final amount.

Step 1: Identify the values.

P=1200,\qquad r=5\%=0.05,\qquad t=2.5

The rate must be written as a decimal, and the time is already in years.

Step 2: Calculate the interest.

I=Prt

I=(1200)(0.05)(2.5)

I=150

The interest earned is 150}$.

Step 3: Find the final amount.

Add the interest to the original principal:

A=P+I

A=1200+150=\boxed{\$1{,}350}

So, after $2.5$ years, the account contains 1{,}350}$.

With simple interest, the interest is proportional to the principal, rate, and time. It does not earn interest on previously earned interest, so the balance increases at a constant rate rather than growing by compound interest.

Learn by doing: Calculate simple interest

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Interest (Simple) - Interest from Principle, Rate, and Time

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