Sure, let's find the amount of money, [tex]\( P \)[/tex], that will generate \[tex]$20 at a 5% interest rate over 5 years, using the formula for simple interest.
The formula for simple interest \(I\) is given by:
\[ I = P \cdot r \cdot t \]
Where:
- \(I\) is the interest earned,
- \(P\) is the principal amount,
- \(r\) is the rate of interest per year, and
- \(t\) is the time in years.
In order to find \(P\), we rearrange the formula to solve for \(P\):
\[ P = \frac{I}{r \cdot t} \]
Now, let's plug in the values given:
- \(I = 20\) dollars,
- \(r = 0.05\) (since 5% as a decimal is 0.05),
- \(t = 5\) years.
Substitute these values into the formula:
\[ P = \frac{20}{0.05 \cdot 5} \]
First, compute \(0.05 \cdot 5\):
\[ 0.05 \cdot 5 = 0.25 \]
Next, divide \(20\) by \(0.25\):
\[ P = \frac{20}{0.25} = 80 \]
So, the amount of money \(P\) that will generate \$[/tex]20 at a 5% interest rate over 5 years is:
[tex]\[
\boxed{80.00}
\][/tex]
