Solving for interest rate in a financial equation with exponent 22

[cs23]

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

 

[tiny-tim]

hi cs23!

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

sorry, not following that

write 1+i in polar form (re^iθ), then you can immediately find (1+i)²² and 1/(1+i)

 

[gb7nash]

Another trick is to substitute a = (1+i)^22. Solve for a. After that, finding i will become much easier.

 

[SammyS]

In LaTeX that's: $$4100=100\frac{(1+i)^{22} - 1}{i(1+i)^{22}}+5000\frac{1}{(1+i)^{22}}$$

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

 

[gb7nash]

In LaTeX that's: $$4100=100\frac{(1+i)^{22} - 1}{i(1+i)^{22}}+5000\frac{1}{(1+i)^{22}}$$

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

Ah, I didn't notice that one i. My method won't work.

 

[SammyS]

Ah, I didn't notice that one i. My method won't work.

Well, it will make simplifying a little easier.... maybe not much.

 

[SammyS]

It probably needs to be done graphically or numerically.

 

[SteamKing]

For clarification, you should state whether i = sqrt (-1) or if i represents an interest rate in some type of compounding interest problem.