Gregalton

Gregalton, how is your secret harmfull email conspiracy against me going??

Gregalton, how is your secret harmfull email conspiracy against me going??[1]

PennySeven (talk) 10:17, 21 February 2009 (UTC)

Here again is the link for the checkuser request [2] that Satori Son advised you to do.

Good luck with your conspiracy.

PennySeven (talk) 10:39, 21 February 2009 (UTC)

What´s happening mate? How´s the old evil secret email conspiracy going?

Are you and Satori Son having lots of fun secretly plotting how to take me out here on Wikipedia? You know it is impossible. I have many good friends all over the world. So why even waste your time on it?

Anyway, tell us how it is going! :-)

PennySeven (talk) 23:14, 26 February 2009 (UTC)

Good grief, Penny, give it up... --Skyemoor (talk) 17:30, 18 March 2009 (UTC)

PennySeven

Sorry for the delay in replying. I needed a break from wikidrama for a while. After looking at the histories of Nicolaas Smith and PennySeven, I would tend to agree with you that they are the same person. However, I have no problems with a user with a checkered past coming back, as long as they have reformed and agree to play by the rules. I also agree that Constant Purchasing Power Accounting is getting a little out of control, and as it stands now, it's not exactly a credit to wikipedia. However, no one is disputing his version of the article (perhaps because it's an obscure topic), and I'm loathe to get involved in a topic I know little about, except perhaps for style issues. I'll drop PennySeven a note about the issues that you have, but frankly speaking, I'ld rather not get involved in any disputes right now. LK (talk) 17:01, 19 March 2009 (UTC)

'Half-life' formula for a mortgage

Hi

Just wondering if it would be in order for me to contribute the following formula for the 'half life' of a mortgage - ie time taken for the loan to reduce to half its original amount - on the Wiki page for compound interest.

$t={\frac {1}{r}}ln{\frac {1+e^{rT}}{2}}$

Where r is the nominal interest rate (annual) and T is the full term of the loan in years.

Problem is I can't reference this formula since I have derived it for myself. Maybe there is a more authoritative source that you know of - presuming someone has done this before !?

Neil Parker (talk) 16:19, 23 April 2009 (UTC)

It's certainly been done before, I seem to remember having this as an exercise in financial maths. Can't remember the derivation (may have been done with calculators). My math with natural logs is bad and my brain weak, so I won't attest 100% to your maths, but I can see what you've done and it's a straightforward derivation using logs.

If I'm not mistaken: you've taken the basic cash flow of an annuity where instead of PV we have 2X = (C(1-e^(-rT)))/(e^r-1), and another x = [same thing but with small t], double the latter formula for 2x, substitute and cancel out, Bob's your uncle.

Whew. Thanks for letting me get my geek on. All that aside, and sorry in advance for wikilawyering:

I have no objection to that being contributed, but the concept of "half life" probably needs to be referenced. Otherwise it's just an example of how to derive something useful - which again, I have no objection to, but it then becomes a question of whether it's a good example, the best example, whether the derivation is new or original research, blah blah blah. (I would argue it's not, or that it's relatively trivial (for those comfortable with the logs at any rate), but it's more a question of presentation than of content).

Thanks for the fun mind problem, though. I haven't had to put on my knitted ln cap in a while.--Gregalton (talk) 21:08, 23 April 2009 (UTC)

Oh, and having got my pencil out, shouldn't it be:

$t={\frac {1}{r}}ln{\frac {1+e^{-rT}}{2}}$

--Gregalton (talk) 21:17, 23 April 2009 (UTC)

I think the formula is correct as it stands. You can check it out on some test data eg: loan of 1 million for 20 years @ 10%pa compounded monthly. Formula gives half life as 14.34 years: near as d.. to 172 months and using Excel's PV function for the remainder (68 months) we are a tad short of half way at 499401.52. With the minus sign in we get -5.66 years - oh dear! Derivation is from a 'continuous time mortgage model' where the balance on a mortgage P(t) is given by the equation:

$P(t)={\frac {P_{0}(1-e^{-r(T-t)})}{1-e^{-rT}}}$

r=interest rate, T=time period of loan in years and P₀ is the original loan amount. Once again this is something I have derived for myself but no doubt also once again there are more authoritative sources. If not, let me know and I'll write a paper on it! One would think 'continuous time mortgages' would be as well explored a topic as continously compounded interest but not that you would notice on the Internet at any rate. In the context of mortgages, terms such as 'time constant' and 'half life' just don't seem to ring any bells on google.

Neil Parker (talk) 08:52, 24 April 2009 (UTC)

Oh sure, go ahead and test the formula to see if it works! At any rate, your approach is just a slightly different variant on the same continuous time value of money base formulae; probably would get the same result if I was smarter and not doing it late at night.

To be honest, I don't know if there are generalized terms for what you're solving; when I was doing this stuff more frequently, this would have just been an exercise (on which, clearly, I would have done poorly) with no need to give it a name. Everyone else just ignores continuous time and grunts it through in Excel.

I find it interesting but it may not be the right material for wikipedia. thanks for the chance to use continuous time for fun!--Gregalton (talk) 15:36, 24 April 2009 (UTC)

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