Math Problem Solver

\[\frac{1000000 \cdot 0.006 \cdot \left(1 + 0.006\right) \cdot 120}{\left(1 + 0.006\right) \cdot 120 - 1} = \frac{18108000}{2993} = 6050.\overline{1169395255596391580354159705980621450050}\]

\[\begin{aligned}\frac{1000000 \cdot 0.006 \cdot \left(1 + 0.006\right) \cdot 120}{\left(1 + 0.006\right) \cdot 120 - 1}& = 1000000 \cdot \frac{6}{1000} \cdot \left(1 + \frac{6}{1000}\right) \cdot 120 \cdot \frac{1}{\left(1 + \frac{6}{1000}\right) \cdot 120 - 1}\\& = 1000000 \cdot \frac{6}{1000} \cdot \left(1 + \frac{3}{500}\right) \cdot 120 \cdot \frac{1}{\left(1 + \frac{6}{1000}\right) \cdot 120 - 1}\\& = 1000000 \cdot \frac{6}{1000} \cdot \frac{503}{500} \cdot 120 \cdot \frac{1}{\left(1 + \frac{6}{1000}\right) \cdot 120 - 1}\\& = 1000000 \cdot \frac{6}{1000} \cdot \frac{503}{500} \cdot 120 \cdot \frac{1}{\left(1 + \frac{3}{500}\right) \cdot 120 - 1}\\& = 1000000 \cdot \frac{6}{1000} \cdot \frac{503}{500} \cdot 120 \cdot \frac{1}{\frac{503}{500} \cdot 120 - 1}\\& = 1000000 \cdot \frac{6}{1000} \cdot \frac{503}{500} \cdot 120 \cdot \frac{1}{\frac{3018}{25} - 1}\\& = 1000000 \cdot \frac{6}{1000} \cdot \frac{503}{500} \cdot 120 \cdot \frac{1}{\frac{2993}{25}}\\& = 1000000 \cdot \frac{6}{1000} \cdot \frac{503}{500} \cdot \frac{3000}{2993}\\& = \frac{6000000}{1000} \cdot \frac{503}{500} \cdot \frac{3000}{2993}\\& = 6000 \cdot \frac{503}{500} \cdot \frac{3000}{2993}\\& = 6036 \cdot \frac{3000}{2993}\\& = \frac{18108000}{2993}\end{aligned}\]