Simple Interest

Simple interest calculates interest only on the original principal and makes borrowing, saving, time, and rate relationships transparent.

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Cash-flow timing determines how financial quantities accumulate. Dated value markers sit above a timeline and grow across successive comparison dates. The caption beneath the axis requires every cash flow to be moved to one common date before totals are compared.

Simple interest is calculated on the original principal for every time period: $I=Prt$.

The four quantities

In the formula $I=Prt$:

$P$ is principal, the original amount invested or borrowed;
$r$ is the annual interest rate written as a decimal;
$t$ is time in years;
$I$ is interest earned or charged.

The final amount is

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

Why growth is linear

Interest is calculated from the same original principal each period. A $1000$ investment at $6\%$ simple interest earns $60$ every year: $60$, then another $60$, then another $60$. Equal time intervals add equal amounts, so amount versus time graphs as a line.

Solving for principal

Rearrange $I=Prt$:

P=\frac{I}{rt}.

If $150$ interest is earned at $5\%$ over $2$ years, $P=150/[0.05(2)]=1500$ dollars.

Solving for rate or time

The same relationship gives

r=\frac{I}{Pt},\qquad t=\frac{I}{Pr}.

A decimal result for $r$ should be converted back to percent for communication. A time such as $1.5$ years means one year and six months, not one year and five months.

Common mistakes

Using $5$ instead of $0.05$. Divide a percent by $100$ before substitution.

Leaving months as whole years. Match time with the rate period.

Reporting amount when interest was requested. Label both $I$ and $A$.

Applying simple interest to a compounding account. Check whether interest itself earns interest.

Quick self-check

What is the principal?
Is the rate in decimal form?
Do rate and time use matching periods?
Does the question ask for interest or final amount?
Are fees or compounding outside this simple model?