Certainly! To solve for the principal amount [tex]\( P \)[/tex] that will generate [tex]$20 in interest at a 5% interest rate over 5 years, we use the formula for simple interest and solve for \( P \). The given formula for simple interest is \( I = Prt \), where:
- \( I \) is the interest earned,
- \( P \) is the principal amount,
- \( r \) is the interest rate,
- \( t \) is the time period in years.
First, isolate \( P \) in the formula:
\[ I = Prt \]
By rearranging the equation to solve for \( P \), we divide both sides by \( rt \):
\[ P = \frac{I}{rt} \]
Now, we use the given values:
- \( I = 20 \) (the interest earned),
- \( r = 0.05 \) (the interest rate as a decimal),
- \( t = 5 \) (the time in years).
Substituting these values into the equation:
\[ P = \frac{20}{0.05 \times 5} \]
Calculating the denominator first:
\[ 0.05 \times 5 = 0.25 \]
Now, divide the numerator by the denominator:
\[ P = \frac{20}{0.25} \]
Which simplifies to:
\[ P = 80 \]
Therefore, the amount of money, \( P \), that will generate $[/tex]20 at a 5% interest rate over 5 years is $80.
