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 Post subject: Let X = substitutionPosted: Thu, 1 Mar 2012 01:55:45 UTC
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Joined: Sun, 5 Feb 2012 21:05:29 UTC
Posts: 18
Hi can anyone help me simplify this equation by letting X = someNumber, to help me solve this equation.

24500(1+i)^3 - 10000(1+i)^(5/3) + 8000(1+i)^(13/12) = 30309

I would like to simplify it algebraically. Thanks.

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 02:51:28 UTC
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Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3689
Location: Ottawa Ontario
Hi can anyone help me simplify this equation by letting X = someNumber, to help me solve this equation.
24500(1+i)^3 - 10000(1+i)^(5/3) + 8000(1+i)^(13/12) = 30309
I would like to simplify it algebraically. Thanks.

Huh? Not much can be done; let x = 1+i; then:
x^3[16/x^(23/12) - 20/x^(4/3) + 49] = 30309/500

Iteration is required to solve; can't be solved directly;
I got x = ~1.10685, so i = ~0.10685

Future Value of $24,500 @ 10.685% annually for 3 years less: FV of$10,000 @ 10.685% annually for 5/3 years
plus: FV of \$8,000 @ 10.685% annually for 13/12 years

If you don't follow that, then: why are you working with that equation?

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 02:52:10 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX
Hi can anyone help me simplify this equation by letting X = someNumber, to help me solve this equation.

24500(1+i)^3 - 10000(1+i)^(5/3) + 8000(1+i)^(13/12) = 30309

I would like to simplify it algebraically. Thanks.

Write 3=36/12 and 5/3=20/12 then you get:

, but I'm pretty sure you have little chance of getting anything out of this to solve explicitly for i using analytic methods.

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 02:58:14 UTC
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Joined: Sun, 5 Feb 2012 21:05:29 UTC
Posts: 18
Yes, you are right, they are theory of interest problems. I was solving this equation with my TI-89 calculator, and it was taking a long time... I thought I could simplify further, but I guess I can't. Do you have a link to teach me the iteration method by hand? Just curious that's all. Once again, thanks for your help.

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 06:36:05 UTC
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Location: Ottawa Ontario

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 11:11:04 UTC
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Joined: Mon, 19 May 2003 19:55:19 UTC
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Location: Lexington, MA

Quote:
Let X = someNumber, to help me solve this equation.

. . Better?

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 11:22:23 UTC
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Joined: Tue, 20 Oct 2009 18:18:45 UTC
Posts: 33
Location: Lisbon, Portugal
i suggested to pass 1+i to the trigonometric form and see if the simplification could be easier...

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 16:04:11 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX
Soroban wrote:

Quote:
Let X = someNumber, to help me solve this equation.

. . Better?

I think you mean

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 16:04:29 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Voxx wrote:
i suggested to pass 1+i to the trigonometric form and see if the simplification could be easier...

It's not a complex number, if it were, this would be easy.

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 17:26:36 UTC
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Joined: Sun, 24 Jul 2005 20:12:39 UTC
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Location: Ottawa Ontario
Soroban wrote:

. . Better?

No, since the OP is learning financial formulas

If someone is taking first driving lesson,
not the time to show him how to drag race down main street!

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 19:23:59 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX
Denis wrote:
Soroban wrote:

. . Better?

No, since the OP is learning financial formulas

If someone is taking first driving lesson,
not the time to show him how to drag race down main street!

I don't think that's the right metaphor for this. What Soroban is doing is not really that much higher of a skill level required, it's just slightly different methodology. So it's more like learning to drive a car and being asked to drive a motorcycle.

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 Post subject: Re: Let X = substitutionPosted: Thu, 1 Mar 2012 19:36:33 UTC
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Quote:
I think you mean

Of course I did . . . *slap head*

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