if i < -1.2145117607341104e-180

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   39.4
2. Using strategy rm
   39.4
3. Applied add-exp-log to get
   \[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
   39.4
4. Applied pow-exp to get
   \[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
   39.4
5. Applied simplify to get
   \[100 \cdot \frac{e^{\color{red}{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\color{blue}{\log_* (1 + \frac{i}{n}) \cdot n}} - 1}{\frac{i}{n}}\]
   26.8
6. Applied taylor to get
   \[100 \cdot \frac{e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{n \cdot \log_* (1 + \frac{i}{n})} - 1}{\frac{i}{n}}\]
   26.8
7. Taylor expanded around 0 to get
   \[100 \cdot \frac{e^{\color{red}{n \cdot \log_* (1 + \frac{i}{n})}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}} - 1}{\frac{i}{n}}\]
   26.8
8. Applied simplify to get
   \[100 \cdot \frac{e^{n \cdot \log_* (1 + \frac{i}{n})} - 1}{\frac{i}{n}} \leadsto \frac{(e^{n \cdot \log_* (1 + \frac{i}{n})} - 1)^*}{\frac{\frac{i}{n}}{100}}\]
   4.3

---

9. Applied final simplification

if -1.2145117607341104e-180 < i < 4.473202120598828e-100

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   61.5
2. Applied taylor to get
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
   61.3
3. Taylor expanded around 0 to get
   \[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
   61.3
4. Applied simplify to get
   \[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{(i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \frac{100}{\frac{i}{n}}}\]
   21.2
5. Using strategy rm
   21.2
6. Applied associate-/r/ to get
   \[(i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \color{red}{\frac{100}{\frac{i}{n}}} \leadsto (i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \color{blue}{\left(\frac{100}{i} \cdot n\right)}\]
   21.5
7. Applied associate-*r* to get
   \[\color{red}{(i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \left(\frac{100}{i} \cdot n\right)} \leadsto \color{blue}{\left((i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \frac{100}{i}\right) \cdot n}\]
   0.7

if 4.473202120598828e-100 < i < 2.2112333586445987e+100

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   48.9
2. Using strategy rm
   48.9
3. Applied add-exp-log to get
   \[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
   48.9
4. Applied pow-exp to get
   \[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
   48.9
5. Applied simplify to get
   \[100 \cdot \frac{e^{\color{red}{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\color{blue}{\log_* (1 + \frac{i}{n}) \cdot n}} - 1}{\frac{i}{n}}\]
   45.7
6. Applied taylor to get
   \[100 \cdot \frac{e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{n \cdot \log_* (1 + \frac{i}{n})} - 1}{\frac{i}{n}}\]
   45.7
7. Taylor expanded around 0 to get
   \[100 \cdot \frac{e^{\color{red}{n \cdot \log_* (1 + \frac{i}{n})}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}} - 1}{\frac{i}{n}}\]
   45.7
8. Applied simplify to get
   \[100 \cdot \frac{e^{n \cdot \log_* (1 + \frac{i}{n})} - 1}{\frac{i}{n}} \leadsto \frac{(e^{n \cdot \log_* (1 + \frac{i}{n})} - 1)^*}{\frac{\frac{i}{n}}{100}}\]
   6.0

---

9. Applied final simplification

if 2.2112333586445987e+100 < i

1. Started with
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   62.2
2. Applied taylor to get
   \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\frac{\log n - \log i}{n}} - 1}{\frac{i}{n}}\]
   27.8
3. Taylor expanded around inf to get
   \[100 \cdot \frac{\color{red}{e^{\frac{\log n - \log i}{n}} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\frac{\log n - \log i}{n}} - 1}}{\frac{i}{n}}\]
   27.8
4. Applied simplify to get
   \[\color{red}{100 \cdot \frac{e^{\frac{\log n - \log i}{n}} - 1}{\frac{i}{n}}} \leadsto \color{blue}{\frac{(e^{\frac{\log n - \log i}{n}} - 1)^*}{\frac{\frac{i}{100}}{n}}}\]
   1.3