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Tahmar knows the formula for simple interest is [tex]I = Prt[/tex], where [tex]I[/tex] represents the simple interest on an amount of money [tex]P[/tex], for [tex]t[/tex] years at [tex]r[/tex] rate. She transforms the equation to isolate [tex]P: P = \frac{I}{rt}[/tex]. Using this formula, what is the amount of money [tex]P[/tex] that will generate [tex]\$20[/tex] at a [tex]5\%[/tex] interest rate over 5 years?

[tex]\$ \boxed{\phantom{0}}[/tex]


Sagot :

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]