# Thread: Having trouble finding x

1. ## Having trouble finding x

This is a finance question - PVIFA

575 = (1-1/(1+r)^12)/r)×50

2. ## Re: Having trouble finding x

Since 'x' is not in the equation, I guess it can be anything you like!

NonTrivial exercise. Try this:

1) Solve for one fo the 'r's and take a good guess.

$f(r) = r = \frac{50}{575}\left[1 - \frac{1}{(1+r)^{12}}\right]$

You THINK the answer might be around 8% Annual, so give a good try of r = 0.006434

f(0.006434) = 0.006441 -- I am delighted that it was so close. Do it again.
f(0.006441) = 0.006448 -- A little disappointing. It moved 7. Do it again.
f(0.006448) = 0.006455 -- Ack. It moved 7 again!
Well, it's not winning any awards for convergence, but it is getting there. Get a computer program to do more iterations. After a few hundred, it settles down to r = 0.00660 91533 89984 (Sorry, I don't know how to shut off Skype) which leads to an annual rate of around 8.225725%.

That's one way to go about it. There are others.

3. ## Re: Having trouble finding x

Originally Posted by TKHunny
Since 'x' is not in the equation, I guess it can be anything you like!

NonTrivial exercise. Try this:

1) Solve for one fo the 'r's and take a good guess.

$f(r) = r = \frac{50}{575}\left[1 - \frac{1}{(1+r)^{12}}\right]$

You THINK the answer might be around 8% Annual, so give a good try of r = 0.006434

f(0.006434) = 0.006441 -- I am delighted that it was so close. Do it again.
f(0.006441) = 0.006448 -- A little disappointing. It moved 7. Do it again.
f(0.006448) = 0.006455 -- Ack. It moved 7 again!
Well, it's not winning any awards for convergence, but it is getting there. Get a computer program to do more iterations. After a few hundred, it settles down to r = 0.00660 91533 89984 (Sorry, I don't know how to shut off Skype) which leads to an annual rate of around 8.225725%.

That's one way to go about it. There are others.
I don't understand what you mean by, "solve for one of the R's"

4. ## Re: Having trouble finding x

Originally Posted by NeedsHelpp
I don't understand what you mean by, "solve for one of the R's"
Essentially you have to converge on a solution largely by guessing.

6. ## Re: Having trouble finding x

Originally Posted by NeedsHelpp
This is a finance question - PVIFA

575 = (1-1/(1+r)^12)/r)×50
solve 575 &#61; &#40;1-1&#47;&#40;1&#43;r&#41;&#94;12&#41;&#47;r&#41;×5 0 - Wolfram|Alpha