if i < -1.1744444546026074e-05

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   29.2
2. Using strategy rm
   29.2
3. Applied associate-*r/ to get
   \[\color{red}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \leadsto \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}}\]
   29.2

if -1.1744444546026074e-05 < i < 5.513334119482794e+20

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   61.7
2. Applied taylor to get
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
   57.7
3. Taylor expanded around 0 to get
   \[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
   57.7
4. Applied simplify to get
   \[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}}}\]
   13.4
5. Applied taylor to get
   \[\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}} \leadsto 100 \cdot n + 50 \cdot \left(n \cdot i\right)\]
   0.0
6. Taylor expanded around 0 to get
   \[\color{red}{100 \cdot n + 50 \cdot \left(n \cdot i\right)} \leadsto \color{blue}{100 \cdot n + 50 \cdot \left(n \cdot i\right)}\]
   0.0
7. Applied simplify to get
   \[\color{red}{100 \cdot n + 50 \cdot \left(n \cdot i\right)} \leadsto \color{blue}{\left(i \cdot 50 + 100\right) \cdot n}\]
   0.0

if 5.513334119482794e+20 < i

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   50.3
2. Using strategy rm
   50.3
3. Applied add-cube-cbrt to get
   \[100 \cdot \frac{\color{red}{{\left(1 + \frac{i}{n}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{{\left(\sqrt[3]{{\left(1 + \frac{i}{n}\right)}^{n}}\right)}^3} - 1}{\frac{i}{n}}\]
   50.4
4. Applied taylor to get
   \[100 \cdot \frac{{\left(\sqrt[3]{{\left(1 + \frac{i}{n}\right)}^{n}}\right)}^3 - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot \left({n}^2 \cdot {\left(\log n\right)}^2\right) + \left(\frac{1}{2} \cdot \left({n}^2 \cdot {\left(\log i\right)}^2\right) + \left(n \cdot \log i + \left(\frac{1}{2} \cdot \left({n}^{3} \cdot \left({\left(\log n\right)}^2 \cdot \log i\right)\right) + \left(\frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log i\right)}^{3}\right) + \left(\frac{{n}^2}{i} + \frac{{n}^{3} \cdot \log i}{i}\right)\right)\right)\right)\right)\right) - \left({n}^2 \cdot \left(\log n \cdot \log i\right) + \left(n \cdot \log n + \left(\frac{1}{2} \cdot \left({n}^{3} \cdot \left(\log n \cdot {\left(\log i\right)}^2\right)\right) + \left(\frac{1}{2} \cdot \frac{{n}^{3}}{{i}^2} + \left(\frac{{n}^{3} \cdot \log n}{i} + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)\right)\right)\right)}{\frac{i}{n}}\]
   4.6
5. Taylor expanded around 0 to get
   \[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot \left({n}^2 \cdot {\left(\log n\right)}^2\right) + \left(\frac{1}{2} \cdot \left({n}^2 \cdot {\left(\log i\right)}^2\right) + \left(n \cdot \log i + \left(\frac{1}{2} \cdot \left({n}^{3} \cdot \left({\left(\log n\right)}^2 \cdot \log i\right)\right) + \left(\frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log i\right)}^{3}\right) + \left(\frac{{n}^2}{i} + \frac{{n}^{3} \cdot \log i}{i}\right)\right)\right)\right)\right)\right) - \left({n}^2 \cdot \left(\log n \cdot \log i\right) + \left(n \cdot \log n + \left(\frac{1}{2} \cdot \left({n}^{3} \cdot \left(\log n \cdot {\left(\log i\right)}^2\right)\right) + \left(\frac{1}{2} \cdot \frac{{n}^{3}}{{i}^2} + \left(\frac{{n}^{3} \cdot \log n}{i} + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)\right)\right)\right)}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot \left({n}^2 \cdot {\left(\log n\right)}^2\right) + \left(\frac{1}{2} \cdot \left({n}^2 \cdot {\left(\log i\right)}^2\right) + \left(n \cdot \log i + \left(\frac{1}{2} \cdot \left({n}^{3} \cdot \left({\left(\log n\right)}^2 \cdot \log i\right)\right) + \left(\frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log i\right)}^{3}\right) + \left(\frac{{n}^2}{i} + \frac{{n}^{3} \cdot \log i}{i}\right)\right)\right)\right)\right)\right) - \left({n}^2 \cdot \left(\log n \cdot \log i\right) + \left(n \cdot \log n + \left(\frac{1}{2} \cdot \left({n}^{3} \cdot \left(\log n \cdot {\left(\log i\right)}^2\right)\right) + \left(\frac{1}{2} \cdot \frac{{n}^{3}}{{i}^2} + \left(\frac{{n}^{3} \cdot \log n}{i} + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)\right)\right)\right)}}{\frac{i}{n}}\]
   4.6
6. Applied simplify to get
   \[100 \cdot \frac{\left(\frac{1}{2} \cdot \left({n}^2 \cdot {\left(\log n\right)}^2\right) + \left(\frac{1}{2} \cdot \left({n}^2 \cdot {\left(\log i\right)}^2\right) + \left(n \cdot \log i + \left(\frac{1}{2} \cdot \left({n}^{3} \cdot \left({\left(\log n\right)}^2 \cdot \log i\right)\right) + \left(\frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log i\right)}^{3}\right) + \left(\frac{{n}^2}{i} + \frac{{n}^{3} \cdot \log i}{i}\right)\right)\right)\right)\right)\right) - \left({n}^2 \cdot \left(\log n \cdot \log i\right) + \left(n \cdot \log n + \left(\frac{1}{2} \cdot \left({n}^{3} \cdot \left(\log n \cdot {\left(\log i\right)}^2\right)\right) + \left(\frac{1}{2} \cdot \frac{{n}^{3}}{{i}^2} + \left(\frac{{n}^{3} \cdot \log n}{i} + \frac{1}{6} \cdot \left({n}^{3} \cdot {\left(\log n\right)}^{3}\right)\right)\right)\right)\right)\right)}{\frac{i}{n}} \leadsto \frac{\left(\left(\frac{1}{2} \cdot n\right) \cdot n\right) \cdot \left(\log n \cdot \log n + \log i \cdot \log i\right) + \left(\left(\left(\left(\frac{n}{i} \cdot n + \frac{\log i \cdot {n}^3}{i}\right) + {\left(\log i\right)}^3 \cdot \left(\frac{1}{6} \cdot {n}^3\right)\right) + \log i \cdot \left(n + \left(\frac{1}{2} \cdot {n}^3\right) \cdot \left(\log n \cdot \log n\right)\right)\right) - \left(\left(\left(\log i \cdot \left(\left(n \cdot n\right) \cdot \log n\right) + \log n \cdot n\right) + \left(\left(\frac{1}{6} \cdot {n}^3\right) \cdot {\left(\log n\right)}^3 + \frac{{n}^3}{i} \cdot \log n\right)\right) + \left(\left(\log i \cdot \log i\right) \cdot \left({n}^3 \cdot \log n\right) + \frac{{n}^3}{i \cdot i}\right) \cdot \frac{1}{2}\right)\right)}{\frac{\frac{i}{n}}{100}}\]
   4.5

---

7. Applied final simplification
8. Applied simplify to get
   \[\color{red}{\frac{\left(\left(\frac{1}{2} \cdot n\right) \cdot n\right) \cdot \left(\log n \cdot \log n + \log i \cdot \log i\right) + \left(\left(\left(\left(\frac{n}{i} \cdot n + \frac{\log i \cdot {n}^3}{i}\right) + {\left(\log i\right)}^3 \cdot \left(\frac{1}{6} \cdot {n}^3\right)\right) + \log i \cdot \left(n + \left(\frac{1}{2} \cdot {n}^3\right) \cdot \left(\log n \cdot \log n\right)\right)\right) - \left(\left(\left(\log i \cdot \left(\left(n \cdot n\right) \cdot \log n\right) + \log n \cdot n\right) + \left(\left(\frac{1}{6} \cdot {n}^3\right) \cdot {\left(\log n\right)}^3 + \frac{{n}^3}{i} \cdot \log n\right)\right) + \left(\left(\log i \cdot \log i\right) \cdot \left({n}^3 \cdot \log n\right) + \frac{{n}^3}{i \cdot i}\right) \cdot \frac{1}{2}\right)\right)}{\frac{\frac{i}{n}}{100}}} \leadsto \color{blue}{\frac{\left(\left(\left({n}^3 \cdot \frac{1}{6}\right) \cdot {\left(\log i\right)}^3 + \left(\frac{\log i}{\frac{\frac{i}{n}}{n \cdot n}} + \frac{n \cdot n}{i}\right)\right) + \left(\left(\left(\log n \cdot \log n\right) \cdot \left({n}^3 \cdot \frac{1}{2}\right) + n\right) \cdot \log i - \left(\log n \cdot \left(\log i \cdot \left(n \cdot n\right) + n\right) + \left(\left({n}^3 \cdot \frac{1}{6}\right) \cdot {\left(\log n\right)}^3 + \frac{{n}^3}{i} \cdot \log n\right)\right)\right)\right) - \left(\left(\frac{{n}^3}{{i}^2} + \left(\log i \cdot \log i\right) \cdot \left(\log n \cdot {n}^3\right)\right) \cdot \frac{1}{2} - \left(\log i \cdot \log i + \log n \cdot \log n\right) \cdot \left(\frac{1}{2} \cdot \left(n \cdot n\right)\right)\right)}{\frac{\frac{i}{100}}{n}}}\]
   4.4