# Help with simplification

1. Jun 27, 2011

### cs23

1. The problem statement, all variables and given/known data

solve for i

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

2. Relevant equations

3. 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

2. Jun 27, 2011

### 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), then you can immediately find (1+i)22 and 1/(1+i)

3. Jun 27, 2011

### gb7nash

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

4. Jun 27, 2011

### SammyS

Staff Emeritus
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: $$4100=100\frac{a - 1}{i\cdot a}+5000\frac{1}{a}$$

5. Jun 27, 2011

### gb7nash

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

6. Jun 27, 2011

### SammyS

Staff Emeritus
Well, it will make simplifying a little easier.

... maybe not much.

7. Jun 27, 2011

### SammyS

Staff Emeritus
It probably needs to be done graphically or numerically.

8. Jun 27, 2011

### SteamKing

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