if i < -0.0006054868320781522 or 3.135592761500106e-05 < i < 1.214996661954119e+104

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 flip-- to get
   \[100 \cdot \frac{\color{red}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\frac{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^2 - {1}^2}{{\left(1 + \frac{i}{n}\right)}^{n} + 1}}}{\frac{i}{n}}\]
   29.3

if -0.0006054868320781522 < i < 3.135592761500106e-05

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   61.7
2. Applied taylor to get
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
   60.2
3. Taylor expanded around 0 to get
   \[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
   60.2
4. Applied simplify to get
   \[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}}}\]
   14.2
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 1.214996661954119e+104 < i < 1.5778042482736102e+150

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   55.7
2. Applied taylor to get
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
   49.1
3. Taylor expanded around 0 to get
   \[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
   49.1
4. Applied simplify to get
   \[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}}}\]
   49.1
5. Using strategy rm
   49.1
6. Applied add-exp-log to get
   \[\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\color{red}{\frac{i}{n}}} \leadsto \left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\color{blue}{e^{\log \left(\frac{i}{n}\right)}}}\]
   56.5
7. Applied add-exp-log to get
   \[\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{\color{red}{i \cdot 100}}{e^{\log \left(\frac{i}{n}\right)}} \leadsto \left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{\color{blue}{e^{\log \left(i \cdot 100\right)}}}{e^{\log \left(\frac{i}{n}\right)}}\]
   56.5
8. Applied div-exp to get
   \[\left(\frac{1}{2} \cdot i + 1\right) \cdot \color{red}{\frac{e^{\log \left(i \cdot 100\right)}}{e^{\log \left(\frac{i}{n}\right)}}} \leadsto \left(\frac{1}{2} \cdot i + 1\right) \cdot \color{blue}{e^{\log \left(i \cdot 100\right) - \log \left(\frac{i}{n}\right)}}\]
   56.5
9. Applied add-exp-log to get
   \[\color{red}{\left(\frac{1}{2} \cdot i + 1\right)} \cdot e^{\log \left(i \cdot 100\right) - \log \left(\frac{i}{n}\right)} \leadsto \color{blue}{e^{\log \left(\frac{1}{2} \cdot i + 1\right)}} \cdot e^{\log \left(i \cdot 100\right) - \log \left(\frac{i}{n}\right)}\]
   56.5
10. Applied prod-exp to get
    \[\color{red}{e^{\log \left(\frac{1}{2} \cdot i + 1\right)} \cdot e^{\log \left(i \cdot 100\right) - \log \left(\frac{i}{n}\right)}} \leadsto \color{blue}{e^{\log \left(\frac{1}{2} \cdot i + 1\right) + \left(\log \left(i \cdot 100\right) - \log \left(\frac{i}{n}\right)\right)}}\]
    56.5
11. Applied simplify to get
    \[e^{\color{red}{\log \left(\frac{1}{2} \cdot i + 1\right) + \left(\log \left(i \cdot 100\right) - \log \left(\frac{i}{n}\right)\right)}} \leadsto e^{\color{blue}{\left(\log n + \log 100\right) + \log \left(i \cdot \frac{1}{2} + 1\right)}}\]
    62.5
12. Applied taylor to get
    \[e^{\left(\log n + \log 100\right) + \log \left(i \cdot \frac{1}{2} + 1\right)} \leadsto e^{\left(\log n + \log 100\right) + \left(\left(\log \frac{1}{2} + 2 \cdot \frac{1}{i}\right) - \left(2 \cdot \frac{1}{{i}^2} + \log i\right)\right)}\]
    35.7
13. Taylor expanded around inf to get
    \[e^{\left(\log n + \log 100\right) + \color{red}{\left(\left(\log \frac{1}{2} + 2 \cdot \frac{1}{i}\right) - \left(2 \cdot \frac{1}{{i}^2} + \log i\right)\right)}} \leadsto e^{\left(\log n + \log 100\right) + \color{blue}{\left(\left(\log \frac{1}{2} + 2 \cdot \frac{1}{i}\right) - \left(2 \cdot \frac{1}{{i}^2} + \log i\right)\right)}}\]
    35.7
14. Applied simplify to get
    \[e^{\left(\log n + \log 100\right) + \left(\left(\log \frac{1}{2} + 2 \cdot \frac{1}{i}\right) - \left(2 \cdot \frac{1}{{i}^2} + \log i\right)\right)} \leadsto \frac{\left(\frac{1}{2} \cdot e^{\frac{2}{i}}\right) \cdot \left(100 \cdot n\right)}{i \cdot e^{\frac{\frac{2}{i}}{i}}}\]
    0.4

---

15. Applied final simplification

if 1.5778042482736102e+150 < i

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   32.4
2. Using strategy rm
   32.4
3. Applied div-inv to get
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{red}{\frac{i}{n}}} \leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{i \cdot \frac{1}{n}}}\]
   32.4
4. Applied *-un-lft-identity to get
   \[100 \cdot \frac{\color{red}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{i \cdot \frac{1}{n}} \leadsto 100 \cdot \frac{\color{blue}{1 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}}{i \cdot \frac{1}{n}}\]
   32.4
5. Applied times-frac to get
   \[100 \cdot \color{red}{\frac{1 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{i \cdot \frac{1}{n}}} \leadsto 100 \cdot \color{blue}{\left(\frac{1}{i} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}\right)}\]
   32.4
6. Applied associate-*r* to get
   \[\color{red}{100 \cdot \left(\frac{1}{i} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}\right)} \leadsto \color{blue}{\left(100 \cdot \frac{1}{i}\right) \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}}\]
   32.4
7. Applied simplify to get
   \[\color{red}{\left(100 \cdot \frac{1}{i}\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}} \leadsto \color{blue}{\frac{100}{i}} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}\]
   32.4