Pre-Algebra
Percentage
Simple interest
20 practice questions
0 video lessons
Theory + worked examples
Simple Interest
California Pre-Algebra • Standard 7.RP.3 • Percentage
Simple Interest is a topic in Percentage in the California Common Core State Standards. It is aligned to Standard 7.RP.3, which requires students to calculate simple interest and the total balance.
Simple interest \(I=Prt\) is earned only on the original principal.
Theory
Simple interest is interest paid only on the original principal:
\[I=P\cdot r\cdot t,\]
where \(P\) is the principal, \(r\) the yearly rate (as a decimal), and \(t\) the time in years.
The total balance is \(P+I\).
The simple interest formula.
A worked example.
Simple interest:
\[I=Prt,\qquad \text{total}=P+I\]
Write the rate as a decimal.
How to use simple interest
- Write the rate as a decimal.
- Multiply principal, rate, and time.
- Add to the principal for the total.
- Rearrange to find a missing quantity.
Example 1 — Interest
Find the interest on \(\$800\) at \(4\%\) for \(2\) years.
Solution
Use \(I=Prt\).
| \(800\cdot0.04\cdot2\) | \(=\) | \(\$64\) |
Example 2 — Total
Find the total balance in Example 1.
Solution
Add interest to principal.
| \(800+64\) | \(=\) | \(\$864\) |
Example 3 — Find the rate
\(\$500\) earns \(\$60\) in \(3\) years. Find the rate.
Solution
Solve \(I=Prt\) for \(r\).
| \(r\) | \(=\) | \(\dfrac{60}{500\cdot3}=0.04=4\%\) |
Example 4 — Find the time
\(\$1000\) at \(5\%\) earns \(\$250\). Find the time.
Solution
Solve for \(t\).
| \(t\) | \(=\) | \(\dfrac{250}{1000\cdot0.05}=5\text{ years}\) |
Common pitfalls
Convert the rate to a decimal first.
Time is in years — convert months.
Interest is only on the principal, not on interest.
Frequently asked questions
What is the simple interest formula?
\(I=Prt\).
Is interest earned on interest?
No — only on the principal.
Interest on \(\$800\) at \(4\%\) for \(2\) years?
\(\$64\).
How do I write the rate?
As a decimal.
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