Sure, let's solve this step-by-step:
1. Given Information:
- Simple Interest ([tex]$I$[/tex]) = [tex]$20
- Interest Rate ($[/tex]r[tex]$) = 5% = 0.05
- Time ($[/tex]t[tex]$) = 5 years
- We need to find the principal amount ($[/tex]P[tex]$).
2. Formula for Simple Interest:
The formula for simple interest is given by:
\[
I = Prt
\]
where:
- $[/tex]I[tex]$ is the simple interest.
- $[/tex]P[tex]$ is the principal amount.
- $[/tex]r[tex]$ is the interest rate.
- $[/tex]t[tex]$ is the time in years.
3. Isolate $[/tex]P[tex]$:
We need to solve the equation for the principal amount $[/tex]P[tex]$. So, we rearrange the formula:
\[
P = \frac{I}{rt}
\]
4. Substitute the Given Values:
- $[/tex]I = 20[tex]$
- $[/tex]r = 0.05[tex]$
- $[/tex]t = 5[tex]$
Plug these values into the formula:
\[
P = \frac{20}{0.05 \times 5}
\]
5. Calculate the Principal Amount:
First, compute the denominator:
\[
0.05 \times 5 = 0.25
\]
Then, divide the interest by this product:
\[
P = \frac{20}{0.25} = 80
\]
So, the principal amount $[/tex]P[tex]$ that will generate $[/tex]20 at a 5% interest rate over 5 years is $80.
