(1 + 0.006)120 / ((1 + 0.006)120 - 1)

asked by guest
on Sep 20, 2024 at 10:40 pm



You asked:

Evaluate the expression: \(\frac{\left(1 + 0.006\right) \cdot 120}{\left(1 + 0.006\right) \cdot 120 - 1}\)

MathBot Answer:

\[\frac{\left(1 + 0.006\right) \cdot 120}{\left(1 + 0.006\right) \cdot 120 - 1} = \frac{3018}{2993} = 1.\overline{0083528232542599398596725693284330103575}\]

\[\begin{aligned}\frac{\left(1 + 0.006\right) \cdot 120}{\left(1 + 0.006\right) \cdot 120 - 1}& = \left(1 + \frac{6}{1000}\right) \cdot 120 \cdot \frac{1}{\left(1 + \frac{6}{1000}\right) \cdot 120 - 1}\\& = \left(1 + \frac{3}{500}\right) \cdot 120 \cdot \frac{1}{\left(1 + \frac{6}{1000}\right) \cdot 120 - 1}\\& = \frac{503}{500} \cdot 120 \cdot \frac{1}{\left(1 + \frac{6}{1000}\right) \cdot 120 - 1}\\& = \frac{503}{500} \cdot 120 \cdot \frac{1}{\left(1 + \frac{3}{500}\right) \cdot 120 - 1}\\& = \frac{503}{500} \cdot 120 \cdot \frac{1}{\frac{503}{500} \cdot 120 - 1}\\& = \frac{503}{500} \cdot 120 \cdot \frac{1}{\frac{3018}{25} - 1}\\& = \frac{503}{500} \cdot 120 \cdot \frac{1}{\frac{2993}{25}}\\& = \frac{503}{500} \cdot \frac{3000}{2993}\\& = \frac{3018}{2993}\end{aligned}\]

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