algebra equation

ecstyle · #1 $Old$ May 11th, 2008, 11:33 PM

I am trying to solve for the variable i but I can't seem to do it. I've tried various ways but get totally lost towards the end.

Here is the equation:
(Note: x is not a variable, it indicates multiplication here)

10.5754 x i = 1 -[1/(1+i)^12]

I know that the answer is .02 or 2% but I can't seem to figure this out and its driving me crazy.

Any suggestions or help is greatly appreciated!

abender · #2 $Old$ May 12th, 2008, 12:02 AM

Is a teacher or textbook actually giving you algebra problems that ask you to solve for i??? And using x as the multiplication operator? The choice of variables /operator symbols is quite bizarre. Nonetheless, while that is important, you probably did not come here to hear that. Here's what's up:

10.5754 x i = 1 -[1/(1+i)^12]

So, we have 10.5754i = 1 - [1/(1+i)^12]

If this is what you mean, then you should get 13 solutions, however, 11 of them will be complex (meaning using of "i"), another should be zero, and the final solution (13th solution) is almost .02. In fact, it is something along the lines of .0199991 per some online calculator I just grabbed. This 0.199991, or simply 0.2 solution is the only real positive solution you get. I this what you were looking for? Are you sure this was how the problem was assigned?

-Andy

abender · #3 $Old$ May 12th, 2008, 12:04 AM

Again, I must reiterate how "wrong" it is to use i as a variable in this context. I should be reserved for the square root of negative 1. i is "imaginary" Moreover, using x as the multiplication operator is equally egregious.
Take care,
-Andy

Reckoner · #4 $Old$ May 12th, 2008, 12:25 AM

Quote:

Originally Posted by ecstyle $View Post$

I am trying to solve for the variable i but I can't seem to do it. I've tried various ways but get totally lost towards the end.

Here is the equation:
(Note: x is not a variable, it indicates multiplication here)

10.5754 x i = 1 -[1/(1+i)^12]

I know that the answer is .02 or 2% but I can't seem to figure this out and its driving me crazy.

Any suggestions or help is greatly appreciated!

Maxima gives the real roots as, approximately, $i=-1.779662862165678,\ 0,\text{ and }0.019999092385499$ .

The exact solution would probably require factorization of

$12553\,{i}^{12}+149449\,{i}^{11}+814254\,{i}^{10}+2683318\,{i}^{9}+5952595\,{i}^{8}+9354411\,{i}^{7}+$
$10658868\,{i}^{6}+8845188\,{i}^{5}+5273631\,{i}^{4}+2174095\,{i}^{3}+567358\,{i}^{2}+72294\,i-1691$ ,

which is by no means easy or feasible. Numerical or graphical approximation is the way to go here.

ecstyle · #5 $Old$ May 14th, 2008, 08:45 PM

no this is actually a finance problem and i am solving for i, which is an interest rate. sorry for any confusion this may have caused. i should've stated that earlier, considering the fact that this is a math forum. my apologies..

10.5754i = 1 - [1/(1+i)^12]

As Andy mentioned, the "13th solution" is almost .02 or .0199991 but how do you solve for this?
Do you need a graphical calculator or can you solve it by hand?