(0.00833333*((1+0.00833333)^36))/(((1+0.00833333)^36)-1)*200000

asked by guest
on Nov 23, 2024 at 11:23 pm



You asked:

Evaluate the expression: \(\frac{0.00833333 {\left( 1 + 0.00833333 \right)}^{36}}{{\left( 1 + 0.00833333 \right)}^{36} - 1} \cdot 200000\)

MathBot Answer:

\[\frac{0.00833333 {\left( 1 + 0.00833333 \right)}^{36}}{{\left( 1 + 0.00833333 \right)}^{36} - 1} \cdot 200000 = \frac{1348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281}{208909092748071173130080410379094617685756625922535036402162556218976454731593325018254458981453276865420150521124606536052710068338080371226049558413202956479816463395196592712396881796716762341116824795649408604007374508188151871408664983228139921991359663072937633351349559139078500} \approx 6453.43706317208326800701151178294283\]

\[\begin{aligned}\frac{0.00833333 {\left( 1 + 0.00833333 \right)}^{36}}{{\left( 1 + 0.00833333 \right)}^{36} - 1} \cdot 200000& = \frac{833333}{100000000} \cdot \left(1 + \frac{833333}{100000000}\right)^{36} \cdot \frac{1}{\left(1 + \frac{833333}{100000000}\right)^{36} - 1} \cdot 200000\\& = \frac{833333}{100000000} \cdot \left(\frac{100833333}{100000000}\right)^{36} \cdot \frac{1}{\left(1 + \frac{833333}{100000000}\right)^{36} - 1} \cdot 200000\\& = \frac{833333}{100000000} \cdot \frac{1348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \cdot \frac{1}{\left(1 + \frac{833333}{100000000}\right)^{36} - 1} \cdot 200000\\& = \frac{833333}{100000000} \cdot \frac{1348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \cdot \frac{1}{\left(\frac{100833333}{100000000}\right)^{36} - 1} \cdot 200000\\& = \frac{833333}{100000000} \cdot \frac{1348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \cdot \frac{1}{\frac{1348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} - 1} \cdot 200000\\& = \frac{833333}{100000000} \cdot \frac{1348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \cdot \frac{1}{\frac{348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}} \cdot 200000\\& = \frac{833333}{100000000} \cdot \frac{1348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \cdot \frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281} \cdot 200000\\& = \frac{1123484285584486666844418885697871010105171017300088915880945889020494202165867466633821526819290295022549570429587023417292862726688602964406509264490211658120551933354253676651758254630618483984436703589116876078399715566201647917789552723049414897051025794962119156315742427889954728703697573}{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \cdot \frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281} \cdot 200000\\& = \frac{1348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281}{41781818549614234626016082075818923537151325184507007280432511243795290946318665003650891796290655373084030104224921307210542013667616074245209911682640591295963292679039318542479376359343352468223364959129881720801474901637630374281732996645627984398271932614587526670269911827815700000000} \cdot 200000\\& = \frac{1348181681974056789836018597244884110079849252699807778980246658923256611901685720634874086132782807140182340588440663477016826078756755059989835113322299318664389785781018724389599661396606739424019813914865817240406554842063914326913194032936911051225651444215120673627160364332091407281}{208909092748071173130080410379094617685756625922535036402162556218976454731593325018254458981453276865420150521124606536052710068338080371226049558413202956479816463395196592712396881796716762341116824795649408604007374508188151871408664983228139921991359663072937633351349559139078500}\end{aligned}\]

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