Help with simplification

  • Thread starter cs23
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  • #1
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Homework Statement



solve for i

4100=100{[(1+i)^22 - 1]/i(1+i)^22} + 5000[1/(1+i)^22]



Homework Equations





The Attempt at a Solution



4100=100{/ i} + 5000[1/(1+i)^22]
4100= 100+5000[1/i + 1/(1+i)^22]
4100=5100[1/(1+ i)^23]
0.803=[1/(1+ i)^23]
(1+ i)^23= 1/0.803=1.24

i= 23 sqrt(1.24) -1
 

Answers and Replies

  • #2
tiny-tim
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hi cs23! :smile:

(have a square-root: √ and try using the X2 icon just above the Reply box :wink:)

sorry, not following that :confused:

write 1+i in polar form (re), then you can immediately find (1+i)22 and 1/(1+i) :smile:
 
  • #3
gb7nash
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Another trick is to substitute a = (1+i)^22. Solve for a. After that, finding i will become much easier.
 
  • #4
SammyS
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In LaTeX that's: [tex]4100=100\frac{(1+i)^{22} - 1}{i(1+i)^{22}}+5000\frac{1}{(1+i)^{22}}[/tex]

Following gb7nash's suggestion this becomes: [tex]4100=100\frac{a - 1}{i\cdot a}+5000\frac{1}{a}[/tex]
 
  • #5
gb7nash
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In LaTeX that's: [tex]4100=100\frac{(1+i)^{22} - 1}{i(1+i)^{22}}+5000\frac{1}{(1+i)^{22}}[/tex]

Following gb7nash's suggestion this becomes: [tex]4100=100\frac{a - 1}{i\cdot a}+5000\frac{1}{a}[/tex]

Ah, I didn't notice that one i. My method won't work. :frown:
 
  • #6
SammyS
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Ah, I didn't notice that one i. My method won't work. :frown:
Well, it will make simplifying a little easier.


... maybe not much.
 
  • #7
SammyS
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It probably needs to be done graphically or numerically.
 
  • #8
SteamKing
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For clarification, you should state whether i = sqrt (-1) or if i represents an interest rate in some type of compounding interest problem.
 

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