(1.02^12-1)/0.02

asked by guest
on Jan 22, 2025 at 4:52 am



You asked:

Evaluate the expression: \(\frac{{1.02}^{12} - 1}{0.02}\)

MathBot Answer:

\[\frac{{1.02}^{12} - 1}{0.02} = \frac{65488719375621415601}{4882812500000000000} = 13.4120897281272659150848\]


\[\begin{aligned}\frac{{1.02}^{12} - 1}{0.02}& = \left(\left(1 + \frac{2}{100}\right)^{12} - 1\right) \cdot \frac{1}{\frac{2}{100}}\\& = \left(\left(1 + \frac{1}{50}\right)^{12} - 1\right) \cdot \frac{1}{\frac{2}{100}}\\& = \left(\left(\frac{51}{50}\right)^{12} - 1\right) \cdot \frac{1}{\frac{2}{100}}\\& = \left(\frac{309629344375621415601}{244140625000000000000} - 1\right) \cdot \frac{1}{\frac{2}{100}}\\& = \frac{65488719375621415601}{244140625000000000000} \cdot \frac{1}{\frac{2}{100}}\\& = \frac{65488719375621415601}{244140625000000000000} \cdot \frac{1}{\frac{1}{50}}\\& = \frac{65488719375621415601}{4882812500000000000}\end{aligned}\]