1-(1+ \dfrac{ .06 }{ 2 } ) ^ { -2 \times 5 }

asked by guest
on Nov 28, 2024 at 1:21 am



You asked:

Evaluate the expression: \(1 - {\left( 1 + \frac{.06}{2} \right)}^{-2 \cdot 5}\)

MathBot Answer:

\[1 - {\left( 1 + \frac{.06}{2} \right)}^{-2 \cdot 5} = \frac{34391637934412192049}{134391637934412192049} \approx 0.25590608510327488688132408418099\]

\[\begin{aligned}1 - {\left( 1 + \frac{.06}{2} \right)}^{-2 \cdot 5}& = 1 - \left(1 + \frac{6}{100} \cdot \frac{1}{2}\right)^{-2 \cdot 5}\\& = 1 - \left(1 + \frac{6}{200}\right)^{-2 \cdot 5}\\& = 1 - \left(1 + \frac{3}{100}\right)^{-2 \cdot 5}\\& = 1 - \left(\frac{103}{100}\right)^{-2 \cdot 5}\\& = 1 - \frac{1}{\left(\frac{103}{100}\right)^{10}}\\& = 1 - \frac{100000000000000000000}{134391637934412192049}\\& = \frac{34391637934412192049}{134391637934412192049}\end{aligned}\]

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