Algebra
Financial mathematics
Simple interest
20 practice questions
2 video lessons
Theory + worked examples
Theory
Simple interest is a fixed percent of the principal each year:
\[I=P\,r\,t,\]
where \(P\) is the principal, \(r\) the rate (as a decimal), and \(t\) the time in years. The total is \(P+I\).
Convert the percent to a decimal before using \(r\).
The simple interest formula.
A worked example.
Simple interest:
\[I=Prt,\qquad \text{total}=P+I\]
Rate is a decimal: \(5\%=0.05\).
How to use simple interest
- Identify \(P\), \(r\) (as a decimal), and \(t\).
- Multiply: \(I=Prt\).
- Add to the principal for the total.
- Rearrange to solve for a missing value.
Example 1 — Find the interest
Find the simple interest on \(\$1000\) at \(5\%\) for \(3\) years.
Solution
Use \(I=Prt\).
| \(I\) | \(=\) | \(1000(0.05)(3)\) |
| \(=\) | \(\$150\) |
Example 2 — Find the total
What is the total amount after \(3\) years?
Solution
Add the interest to the principal.
| \(\text{total}\) | \(=\) | \(1000+150=\$1150\) |
Example 3 — Convert the rate
Write \(4\%\) as a decimal rate.
Solution
Divide by \(100\).
| \(r\) | \(=\) | \(0.04\) |
Example 4 — Solve for time
How long for \(\$500\) at \(6\%\) to earn \(\$90\) interest?
Solution
Solve \(I=Prt\) for \(t\).
| \(90\) | \(=\) | \(500(0.06)t\) |
| \(t\) | \(=\) | \(3\ \text{years}\) |
Common pitfalls
Use a decimal rate: \(5\%=0.05\).
Time is in years to match an annual rate.
Interest is not the total — add the principal.
Frequently asked questions
What is the simple interest formula?
\(I=Prt\).
How do you write \(5\%\) for the formula?
As \(0.05\).
How do you find the total amount?
Add the interest to the principal.
What is the principal?
The starting amount of money.
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