From: john boyle 
Newsgroups: uk.finance
Subject: Re: annual equivalent of weekly return on investment
Date: Mon, 18 Aug 2003 19:05:54 +0100

In message , Ronald
Raygun  writes
>Jim wrote:
>
>> The original statement wasn't mis-quoted. This is social security benefits
>> we're talking about...( the new savings credit to retirement
>> pension)....the first £6000 of your capital is ignored, additional capital
>> will reduce the credit, on the assumption that every £500 will produce an
>> income of £1 a week.
>>
>> My questions were :
>> 1) what is the annual equivalent of the weekly return
>
>Presumably since benefits are paid weekly, then the credit would
>be added weekly, but reduced by the assumed weekly income, so
>the annual equivalent is of limited relevance, since the income
>produced by the capital would be assumed to get spent each week,
>not added to the capital.
>
>Chances are it would simply be N times the weekly income, but what
>N would be is anyone's guess.  It could either be 52 or 53 (depending
>on how many weeks any given year would be deemed to contain, income
>from a year-straddling week being allocated wholly to the old year
>or the new), or it could be 365/7 or 366/7 (depending on whether the
>year in question contains a leap day) or it could be 365.25/7 or
>maybe even 365.2425/7.
>
>> 2) If the £1 a week were re-invested, what would be the annual return.
>
>That's a tricky one.  Normally, a return of £1 per week per £500, i.e.
>0.2%pw would be equivalent to between 10.95% and 11.17% depending on
>which N you use.
>
>On the other hand, if you apply the same income assumption rules,
>then if your capital is between £6001 and £6448, it will "generate"
>income of £1 each week even if you reinvest it each week, and you'd
>end up with £6500, a return of £52 on anywhere between £1 and £448,
>being between 11.6% and 5200%.  But if you started with, say, £6474,
>this would be assumed to earn £1 for each of the first 26 weeks and
>£2 for each of the other 26 weeks.  That'd be roughly equivalent to
>a return of £78 on £474, nearly 16.5%.
>
>> In that context, you have to ignore the first £6000, or the return
>> would be variable.
>
>I think you just have to accept that the return *is* variable, if
>only because of the obviously crazy 5200%.
>

Having now read the gov web site, I can see that whilst my original
assertion wasnt quite right, in essence it was in so far as the whilst
the calculation ignores the first £6000, in coming to the conclusion
that each £500 over the £6k provides £1 per week then :-

        They are taking the assumed 'income' from the first £6k into
account and assuming income from £6.5k

        AND/OR they are assuming that you are cutting into capital, just
like an annuity would.
-- 
john boyle