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Math101learn.math101.caSimple Interest
Simple interest calculates interest only on the original principal and makes borrowing, saving, time, and rate relationships transparent.
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
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.
Calculating interest and amount
Keep interest and final amount distinct. A question asking “how much interest?” wants $I$; “how much altogether?” wants $A$.
Matching time and rate
An annual rate requires time in years. Nine months is $9/12=0.75$ years. For $800$ at $7\%$ for nine months,
If a rate is explicitly monthly, time should be in months. The rate period and time unit must match.
Solving for principal
Rearrange $I=Prt$:
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
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.
Comparing offers
Simple interest supports fair comparison only when principal, rate period, time, and fees are understood. A loan advertising a low rate may still have charges outside the formula. Real Canadian consumer products can use different compounding, payment schedules, and disclosure rules, so treat $I=Prt$ as a mathematical model and read actual terms.
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?
Related topics
Explore the idea
Sequence explorer
Change one quantity at a time and connect what moves to Simple Interest.
Try it yourself
Hints are part of learning. Open one whenever it makes the next step feel possible.
Find the simple interest on $2400 at 4.5% per year for 3 years.
- I = 2400(0.045)(3)
- I = 324
End of lesson
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