- Started with
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
49.4
- Using strategy
rm 49.4
- Applied add-exp-log to get
\[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
49.4
- Applied pow-exp to get
\[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
49.4
- Applied expm1-def to get
\[100 \cdot \frac{\color{red}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
43.5
- Applied taylor to get
\[100 \cdot \frac{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}{\frac{i}{n}} \leadsto 100 \cdot \frac{n \cdot (e^{\log \left(\frac{i}{n} + 1\right) \cdot n} - 1)^*}{i}\]
45.6
- Taylor expanded around 0 to get
\[100 \cdot \color{red}{\frac{n \cdot (e^{\log \left(\frac{i}{n} + 1\right) \cdot n} - 1)^*}{i}} \leadsto 100 \cdot \color{blue}{\frac{n \cdot (e^{\log \left(\frac{i}{n} + 1\right) \cdot n} - 1)^*}{i}}\]
45.6
- Applied simplify to get
\[100 \cdot \frac{n \cdot (e^{\log \left(\frac{i}{n} + 1\right) \cdot n} - 1)^*}{i} \leadsto \frac{n \cdot 100}{i} \cdot (e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1)^*\]
15.0
- Applied final simplification
