Conference nyoss1::market_investing

I think part of the idea is not to put $1 million into savings, but to start
saving and let it compound so it will read $1 million (or whatever).

Elaine

  Well, if you were to invest your $5k (+2% matching) per year in the 401k 
  Growth fund making about "normal" growth of 10% over the next 25 years (63 
  years old) you'd have .65 Million...Not bad!  Some years are better than 
  others, for instance this year I've averaged 35% growth for my stock funds, 
  16% for Bond Funds and 8+% for "fixed" incomes.  If you watch your
  numbers carefully you can get more than 10%  Also, if you can get your
  max in your 401k (plus matching) making 10%, you end up with $1.2m !
  
  You can make it, just have to stretch to sock away as much 401k money as
  you can!  Once the 401k money no longer "hurts", turn to other
  investments such as those covered in this conference.
  
  Good Luck
  

    If you get to the point where you can contribute the max to your 401K,
    also look at IRAs.  Although the amount you contribute to an
    IRA is after tax, the interest is tax-deferred.  Also, I believe
    you can contribute more than the $2000 individual contribution
    because your wife doesn't have a non-housewife job, although I've
    forgotten what the limit is and whether it's a joint account or
    what;  the IRS 800 number should be able to tell you or send you
    an IRA pamphlet.
    
    .1 is right about compounding being the ticket.  Snarf up some
    freebie retirement planning booklets from Schwab or Twentieth Century,
    etc. from their 800 numbers, they go into this all in detail, plus
    suggestions for what risk level of investment mix you should look at,
    depending on your age and family circumstances.  There are probably 
    informative articles on planning for college expenses in back issues of
    Money Magazine or similar magazines that are available at most libraries.
    
    At 38, there is still time to get things in order.
    

Whatever you do, start now!

 Don't let the numbers overwhelm you.  If for the next 25 years
 you put that lousy $7K into a 401K (e.g. SAVE), and your
 investments average a 7.5% annual return, you'll end up with
 around $500K.  If you manage to get 10%, you'll end up with around
 $750K.

Whatever you do, start now!

 Pay yourself first.  Figure out what you must pay (mortgage, 
 etc.), then set aside something for savings (SAVE), then figure
 out how to live on the rest.  Now, with one income, wife and
 three kids, this can be tough, but ya gotta do it! 

Whatever you do, start now!

 Don't save - invest.  Most of your retirement "savings" should go
 into stocks or stock mutual funds.  Stocks historically beat 
 inflation, while the "safer" savings vehicles guarantee that 
 you'll end up behind.

Whatever you do, start now!

 Read a personal finance book.  "Mutual Funds for Dummies" and 
 "The Wealthy Barber" were recommended a couple of weeks back. 
 There are lots of good ideas that are easy to implement.

Whatever you do, start now!

 You really do have time.  If you start now, things will soon be
 a lot better. 

Good luck,

Wes

    
    	And whatever you do, don't panic.
    
    	Relax, I didn't get serious with my savings until I was 41. Paying
    	attention, maxing my 401 (k), shoving extra money into an IRA,
    	also funding my wife's IRA (non-working also), am now at 49 - and
    	am close to $130K in retirement funds.
    
    	My math shows that compounding at just 9% annually at 65 I'll have
    	$516,000 and that is without putting another dime in betwwen now
    	and  then.
    
    	When Albert Einstein was asked the greatest mathematical formula
    	known to man, he said "Compound interest".
    
    	Start saving tomorrow, relax, and enjoy...
    
    
    		the Greyhawk

>     If you get to the point where you can contribute the max to your 401K,
>     also look at IRAs.  Although the amount you contribute to an
>     IRA is after tax, the interest is tax-deferred.
                            ^^^^^^^^

	Well given the age of the base noter they should still be investing
	in more than "income" investments (ie. "growth" stocks, etc, as
	capital gains are also tax defered)

I also recommend that you buy "The Wealthy Barber", read it, and pay
attention, i.e., do what seems prudent (like pay yourself first). That
book was written for you!

Pete

Simply echoing the previous, but from a different slant...I'm 38, also have 
young kids, and am in a similar (but of course, NOT identical) situation.

Max the 401k, invest in growth (little if any in "safe" GICs or MMFs in SAVE)

Put the $2k, or $2.15k, in the tax-deferred IRA, same invest strategy as 
401K.

$7-10k per year over ~25 years at ~7-12% (I know, a W I D E range, but 
frankly, a growth stock strategy over that time frame can exceed 10%) and the 
retirement apartment may not be too dingy.  Who knows, the DEC pension + Soc 
Security may even survive to help. So will other investments...home equity is 
another tax-deferred "savings" vehicle. Invest outside of sheltered vehicles 
in a similar fashion, with the caveat of planning for the kids edu (thats a 
big caveat, tho... :-)

Actually, I don't know about soc security, but the pension WILL help, whether 
it survices or is rolled into a SAVE-like program.

Learn from the past, plan for the future, and live/enjoy the present.

SteveS

    We have 2 incomes, young kids, similar age group (ok, my husband is,
    I'm younger 8^) ) and I can still relate to your anxiety.
    
    I echo what was said before: start now.  Max out on your 401k, invest
    any extra (it doesn't have to be alot, can you scrape together $50/mo?).
    
    What I find easiest is automatic monthly investing.  If you don't have
    to write that check or drive to the bank it is a lot less painful.  If
    you don't see it, you don't spend it and while you aren't thinking
    about it you are saving.  We do this for our investments and for our
    daughters' college funds (our 3.5 yr old is already saying she wants to
    be a doctor $$$$).  Some funds, like the 20th century funds, waive the
    minimum investment level if you do automatic monthly deposit.  
    
    Yup, there are some months I would kill to have that extra cash (like
    around now with the holidays coming up), but we've learned how to
    manage what's left after the mortgage, bills, etc.  I've learned how to
    be very creative.
    
    Good luck.
    
    /Susan 

    Thanks for the therapy session.  After reading through the notes, I
    took the SAVE brochure thats been sitting on my desk for months and
    enrolled at the maximum level.  Based on my contibution for 25 years at
    an average rate of return, I will sleep a little better tonight.  My
    two year old will have to now justify a diaper change, but it will  be
    worth it.
    
    Thanks for your words of wisdom.
    
    John 

    Additional unsolicited advice :-)  With small children and being the
    sole breadwinner, you need to have life insurance.  People get run
    over by trucks, etc. in the prime of life all the time.
    
    Also, if your wife were to start working outside the home once
    your kids reach, say, junior high school, she'd have ten to fifteen
    years to add additional income and her own 401K contributions to
    the retirement pot.  I'm not sure if this would be helful from
    the point of view of social security (may it continue to exist)
    or not, since i don't know how that works in this situation.
    

re: .10

That was quick!  Congratulations on taking that first step.

Wes

just to give you an idea what time does.
my wife began 401k contributions 3 or so yrs before
me and she makes about 60% of what i make.
yet, her 401k balance is about 9k higher than
mine 'cuz she started much earlier.  also, 100%
of our 401k dollars are in growth funds.  0% in
fixed income funds!  this year alone has made up
for '93 and '94.  we're 30 now, have nearly 40k in
401k, and plan to continue to grow that in addition
to the other investments we have.

i'm: save save save.

she is: buy furnature buy furnature buy buy

i always say, what's wrong with the furnature???
it works!!!  must be a guy thing

    
    Consider the digital stock plan. An easy way to make 15% + or 
    a little less. 

As a matter of fact, I just asume that anyone eligible would be fully
enrolled in the ESPP, unless you know of some other place that will
guarantee an APR of something like 60% (I seem to recall someone
calculated that somewhere, taking into account the weekly cash flows
and all).

> As a matter of fact, I just asume that anyone eligible would be fully
> enrolled in the ESPP, unless you know of some other place that will
> guarantee an APR of something like 60% .....

	Well I'm certainly fully enrolled, but I've known several
	other engineers who just couldn't afford to have that 10%
	of their salary taken away for a 6 month timeframe due
	to expenses (especially those married and raising children).
	If an engineer on an engineers salary can't afford the
	reduced cash flow, then I'm sure it could be even tougher
	for lower wage earners (and maybe even some of those higher
	wage earners out there :-)

Perhaps some of us could offer a service. If you enroll in ESPP at the
10% level, I'll reimburse you each week 110% of your contribution.
Every 26 weeks you promise to sell the stock you acquire when it is
acquired and send me the check.

Pete

> Perhaps some of us could offer a service. If you enroll in ESPP at the
> 10% level, I'll reimburse you each week 110% of your contribution.
> Every 26 weeks you promise to sell the stock you acquire when it is
> acquired and send me the check.
    
    Actually I've long thought this is something the DCU could finance
    at a profit to themselves AND their customers. This kind of scheme,
    however, probably violates a dozen securities laws so if anybody
    cuts this kind of deal, don't talk about it! (And don't try to argue
    logic here, this is the LAW! :-)
    
      John

Unless you have a really bad credit history, you should be able to get some
kind of loan to make up for the cash flow loss caused by ESPP enrollment.

> Unless you have a really bad credit history, you should be able to get some
> kind of loan to make up for the cash flow loss caused by ESPP enrollment.

	Aren't personal loans at least 10%, if not more?  And if you
	only get 15% (30% annually) on the stock (and prior to this
	past year, the several years before the stock was on a steady
	decline, and some of those buyins when people sold right away
	got less than 15%), and then you pay taxes when you sell it
	right away, and then you have to worry about filling out your
	tax forms, .....

    Take advantage of these 5.9 or 6.9 % visa cards that come in the mail
    on a weekly basis. Most are for 6 months but thats ok with me. I take 
    advantage of this all the time. I've gone thru 15+ cards the last 2
    years and they keep on coming. I'll gladly borrow at 5.9 % to make at
    least 15% anytime..

> Take advantage of these 5.9 or 6.9 % visa cards that come in the mail
> on a weekly basis. Most are for 6 months but thats ok with me. I take 
> advantage of this all the time. I've gone thru 15+ cards the last 2
> years and they keep on coming. I'll gladly borrow at 5.9 % to make at
> least 15% anytime..

	I'd hate to see your credit report ......

> My two year old will have to now justify a diaper change, but it will  be
>    worth it.

Based on my experience with our 2 year old (and two previous siblings) this
justification should happen on a regular, daily basis.

(couldn't resist)
					Mark

    Credit report is long but up to date with no problems. 
    Is there a problem with a long credit report that I dont know about..
    
    -2  this  reply is for.

> Credit report is long but up to date with no problems. 
> Is there a problem with a long credit report that I dont know about..

	I'd certainly be weary of someone with LOTS of credit cards
	if I was a lender (I am a landlord and I'd be weary if you
	were a prospective tenant, but I have a feeling your not
	a renter :-)

    Nope I'm not a renter. I along with the bank own my home. :-)
    	
    	I dont have 15 open cards. I only have 4 active cards now. I take
    the 6-12 months low rate cards but once the intro time expires and the
    cards go up to the 16% range I pay them off with another 5.9 card that
    I request. 
    
    	

RE: .17
>>  > As a matter of fact, I just asume that anyone eligible would be fully
>>  > enrolled in the ESPP, unless you know of some other place that will
>>  > guarantee an APR of something like 60% .....
>>
>> 	 Well I'm certainly fully enrolled, but I've known several
>> 	 other engineers who just couldn't afford to have that 10%
>>	 of their salary taken away for a 6 month timeframe due
>>	 to expenses

    They don't have to start at 10%.  The minimum is only 2%, so if
    they can afford 2%, then they can work up to 10%....

    For example, they enter the program on December 1st for 2%, then
    on June 1st they increase to 4% and use the check from the first
    6 months to offset the additional 2%.  Every six months they
    increase the contribution by 2%, using the proceeds from the
    previous 6 months to offset the "loss" of income.  After 2 years
    they'll be at 10%.

    Of course the hard part is to use the checks that arrive every 6
    months to pay bills instead of buying a big screen TV, etc.

    -dave

	I have a question which is somewhat similar to the current discussion, I
    posted it in the wrong conf (espp) but it fits in here.
    
    	We all know of the rule of 72 which basically states that if you
    take a compounded interest rate and divide it into 72 then that's the
    number of years it will take for the initial investment to double. eg
    if I put 1000 into a savings account at .06 interest it will become
    2000 in 12 years, 4000 in 24 years etc.  No problem so far?
    
    	Now I want to compare this to investing in a mutual fund which
    states that the "rate of return" is 12% over the last 24 years with the
    implication that my 1000 will double in 6 years and in 24 years will
    be (2,4,8) 16000, which would be the case if it was 12% interest
    compounded.  If the $1000 was invested four times a year (75/wk) over that
    period then the end result shows a staggering difference for each type 
    at the end of 24 years.
    
    	Now I open this up for discussion.  
    
    First the "compounding" if that term  could even be used would be monthly, 
    Second Mutual funds don't increase at a constant rate but might go up 1.5% 
    one month and go down .5% another month.  This would seemingly negate this 
    rule of 72 comparison.
    
    	Now if contemplating investing in mutual funds vs banks or cds I
    would guess the the "Rate of return" over past history that the mutual
    fund advertises (not to speak of everything else eg costs) would have 
    to be discounted (say 12% => 9%) to compare with compounded interest
    and the rule of 72.
    
    	But my basic question is who does advertised, past-history, mutual
    fund rates of return truly compare vis a vis the rule of 72 with
    compounded interest rates.

    The rule of 72 is only an approximation, to be used when you don't have
    a calculator and can calculate more exactly.  If the fund had a 12%
    rate of return over the last 24 years then the function balance went
    something like:
    
        Year    Balance
        0       $1,000.00
        1       $1,120.00
        2       $1,254.40
        3       $1,404.93
        4       $1,573.52
        5       $1,762.34
        6       $1,973.82
       12       $3,895.98
       24       $7,689.97
    
    (12% compounded yearly)
    

    You are compounding yearly, compounding daily or even monthly (which is
    closest to the rule of 72) is a different story.  Here are the comp/mo.
    numbers for .12 (using decalc with the default).  Note I use row 71,143
    etc.
    
    APP(1000,0.12/12,1;A1:A1000)                                        
    
    2006.76331 6 years   
    4108.04346 12 yrs
    8409.57324 18 yrs
    17215.2324 24 yrs
    
    But my point is this is "compounding".  Mutual funds valuate shares
    monthly and this can be plus or minus: eg 100 shares buys so much
    stock,bonds,cash in period 1,2...999.  
    
    I just don't believe comparisons with rules of 72 etc which
    generalize compounded interest returns are applicable to mutual funds.
    Or they may be, I just don't know.
    

    I made a mistake in my previous calculation.  The 24 year total should
    be the 18 year total.  The actual 24 year total is close to yours.
    
    > If the $1000 was invested four times a year (75/wk) over that
    > period then the end result shows a staggering difference for each type 
    > at the end of 24 years.
    
    At the end of the 1st quarter you've earned no interest
    
        3 months    $250
        6 months    $257.57 + 250 = $ 507.57
        9 months    $522.96 + 250 = $ 772.96
        1 year      $796.38 + 250 = $1046.37
    
    whereas you assume that your savings account started with the full
    $1000 so at the end of year 1 it has $1,126.82.  But thats a difference
    of on  $80.  You double this difference 4 times and get a final
    difference of about $320.  Does this help?
    
    ------
    
    Multiplication is commutative and associative so you can compute the
    average yearly, monthly, daily rate of return for the stock market and
    compare that against the yearly, monthly, daily rate of return of any
    other investment.  The comparison is good for the period of past.  It
    doesn't explain what happened during subsets of that period.  Nor does
    it predict future behavior.
    
                                August 

    Actually I meant 1000 four times a year in the sense of $4000/yr
    invested every year for 24 years and the resulting differences per each
    point of "interest" being "staggering".
    
    But it is in the difference between compounded interest and the figure
    that Mutual funds give as "rate of return" which was the focus of my
    question.  But from the note in Digital-Investing where the focus was
    in making comparisons with "annualized returns" (eg one basic point of
    comparison) I was curious as to the comparison of the mutual fund
    figures with the "staggering" returns from compounded interest.
    
    	Can I conclude that when Fidelity says that Magellan had a nn%
    return over a 10 year period that they are truly  saying that $1000
    invested 10 years ago would = $1000 Appreciated .nn (eg compounded).
    
    	My other question is more practical and that is: Since the market
    for the last 15 years has shown periods of rapid advance and decline
    along with long moribund periods Mutual funds can "mark" rate of return
    periods to coincide with the positive skews and avoid the negative and
    slow periods.

 >   	Can I conclude that when Fidelity says that Magellan had a nn%
 >   return over a 10 year period that they are truly  saying that $1000
 >   invested 10 years ago would = $1000 Appreciated .nn (eg compounded).
    
    Would Fidelity lie (I mean shade the truth)?  You could always call
    them on the phone an find out exactly what they mean.
    
 >   	My other question is more practical and that is: Since the market
 >   for the last 15 years has shown periods of rapid advance and decline
 >   along with long moribund periods Mutual funds can "mark" rate of return
 >   periods to coincide with the positive skews and avoid the negative and
 >   slow periods.
    
    There is some risk of this but 10 years is a pretty standard measure,
    as are 5 years, 15 years and some others.  Some quote since date of
    inception, especially if they haven't been around 10 years.  I'ld be
    leary of someone quoting some time 12 years a 3 months ago, or someone
    starting their quote just after the crash (er, correction) of whenever
    (87?).
    
    Don't forget to include the effect of taxes.  Unless you invest via a
    tax free account (IRA, SAVE) you'll be paying taxes on dividends and
    other taxable events in the funds.  These can dramatically lower your
    returns.  Of course, they lower your return on your savings account as
    well.
    

    No I wasn't talking about lieing, just what does the investment/mutual
    fund house mean.  What common denominator are they using.  Virtually
    the same question that Jeff and Gim were talking about in dec-inv.
    
    The reason I'm asking is I have heard salespersons make comparisons
    between rates of return using the rule of 72 as an illustration and
    thats fine if the comparison is in interest bearing securities.  I'm
    questioning the comparison with mutual funds and past and projected
    rates of return.

I've started this response about five times, and I'm still not 
sure if your question is getting answered.

If you're looking at the past long-term performance, then you can 
take a stock mutual fund's compound rate of return and plug it 
into the rule of 72 to compare historical returns. Or in another
sense, you can see from these comparisons that, long-term, stocks
outperform bonds and other interest-bearing instruments. 

(Make sure that you're being quoted a equivalent compound rate of 
return.  I've seen funds or magazines quote an "average annual
rate of return".  This doesn't compare, since if you double your 
money in six years, the *compounded* rate is about 12%, and the
*average* rate is 16.7%.)

If you're looking into the future, volatility becomes an issue.
This is one of the reasons that dollar-cost averaging is so
popular.  Periodic redemption should be as popular, but I don't
know if it is.  They both are an attempt to "smooth out"
volatility inherent in stock mutual funds. 

Figure out what return you're looking for, how much 
risk/volatility you're willing to accept, realize that higher
returns usually mean higher risk/volatility, then use these to
choose your investments. 

Wes

              <<< Note 941.36 by NLA0::ONO "The Wrong Stuff" >>>
    <(Make sure that you're being quoted a equivalent compound rate of 
    <return.  I've seen funds or magazines quote an "average annual
    <rate of return".  This doesn't compare, since if you double your 
    <money in six years, the *compounded* rate is about 12%, and the
    <*average* rate is 16.7%.)
    
    This was exactly what I was looking for, a comparison between a rule of
    72 type return with the posted rates of return and the use of terms
    like "average annual".  Mutual fund listings generally do quote 5, 10
    year "rates of return" (actual); are these compound on average annual?
    
    On the subject of investment strategy and the use of 5 and 10 year rrs:
    it would appear that 1992 five year rates might be interesting research
    since that would include the correction.
    
    Finally, our 401k statements show rates as high as 8% for the secure
    investments (I've been in B and before that D so I don't check this
    closely) - does this then compare to a 11,12% mutual fund?

I'm looking at the Fidelity FundsNetwork Q395 Performance 
Directory.  The "average annual return" is  a load-adjusted, 
compound annual total return, including reinvestment of dividends 
and distributions.

Look at the fine print.  It usually tells you.

Wes

    Wes didn 't you say in a previous note that compound annual is quite a
    bit different than compound daily as in interest.  Wouldn't compound
    annual rr (say) of 15% equal about 12% compound daily?

Wasn't me, but 12% compounded monthly yields 12.68%. Compounded
daily, it yields 12.75%.  Not that much difference. 

(I think these numbers are right.  If they're not, I'm sure 
someone will let us know.)

Wes

    You can use the following in DIGICALC:

    A1	(enter the rate, ie. 12% = 12)
    A2  (enter how often it is compounded, ie. daily = 365)
    A3  100*(EXP(A2*LN(1+((A1/100)/A2)))-1) ---> gives APR

    -dave

Add a leading "=" to A3 and it works in Excel too.

    > Wasn't me, but 12% compounded monthly yields 12.68%. Compounded
    > daily, it yields 12.75%.  Not that much difference.
    
    Not much except for one thing: Roundoff error. If you were able to
    carry fractional cents from one period to the next, then daily
    compounding will always outperform monthly. But when banks compute
    interest, they get to keep any fractions of a whole cent. That doesn't
    affect large balances so much, but for balances under (rough guess)
    $5000, it could actually make daily compounding worse than monthly.
    
    To take an extreme example, suppose you had $1.50 in the bank. At 12%
    compounded annually, you'd get a lump disbursement of 18� at the end of
    the year. Compounded monthly, you would get 1.5 � per month (a bit more
    month by month, but still under 2�), rounded
    to 1�, to give a total of 12�. Compounded daily, the fractions would be
    less than 1�, so you'd never get any interest.
    
    All this assumes that the fractional cents are truncated, which was
    the industry practice last time I checked. Some institutions might
    round anything over .5 to the next higher cent, but I've never heard of
    that. But this is why banks were so quick to adopt daily compounding
    back in the early 1980's. They knew that most customer
    balances were low enough that roundoff (truncation, actually) would
    work in their favor.
    				Jim B.

    When I wrote a spreadsheet to calculate my mortgage balance over the
    years I was off by a couple of cents until I rounded the interest due
    to the nearest penny.  So, I assume that the banks round instead of
    truncate.
    
                                August

>     All this assumes that the fractional cents are truncated, which was
>     the industry practice last time I checked. Some institutions might
>     round anything over .5 to the next higher cent, but I've never heard of
>     that. But this is why banks were so quick to adopt daily compounding
>     back in the early 1980's. They knew that most customer
>     balances were low enough that roundoff (truncation, actually) would
>     work in their favor.

The above is not true at the DCU.  According to DCU Operations, the
handling of fractional cents is specified in the truth in lending laws.
At the DCU, interests paid for deposits are rounded and interest charged
on loans are also rounded.  

	1.254 becomes 1.25
        1.255 becomes 1.26

In total, with the large number of accounts,
the net to the credit union might be a few pennies.


Gim

re: -< Rounding at the DCU >-

>       1.254 becomes 1.25
>       1.255 becomes 1.26

I do not doubt that this is actually what DCE does, but, for the purists
among the mathematicians and statisticians who read this, it is NOT rounding.
It is "half adjusting".

In true rounding

        1.254 becomes 1.25
        1.255 becomes 1.25  <----.
        1.256 becomes 1.26       | This is where the
        1.264 becomes 1.26       | difference is.
        1.265 becomes 1.26  <----'
        1.266 becomes 1.26

In words, if the part being dropped is exactly 5, the last digit kept is
chosen to be an even digit.  This is necessary to avoid a bias toward the
higher number.

Re .47        <<< Note 941.47 by STAR::HAMMOND "Charlie Hammond -- ZKO3-04/S23 -- dtn 381-2684" >>>

>In true rounding
>
>        1.254 becomes 1.25
>        1.255 becomes 1.25  <----.
>        1.256 becomes 1.26       | This is where the
>        1.264 becomes 1.26       | difference is.
>        1.265 becomes 1.26  <----'
>        1.266 becomes 1.26
>
>In words, if the part being dropped is exactly 5, the last digit kept is
>chosen to be an even digit.  This is necessary to avoid a bias toward the
>higher number.

In that case, wouldn't 1.255 become 1.26?  Setting 1.255 to 1.25 violates
"the last digit kept is chosen to be an even digit" rule you mention.

I got it wrong.  here is the correctedversion
(changes at |)
                             -< Rounding to even >-

In true rounding

        1.254 becomes 1.25
|       1.255 becomes 1.26  <----.
        1.256 becomes 1.26       | This is where the
        1.264 becomes 1.26       | difference is.
        1.265 becomes 1.26  <----'
|       1.266 becomes 1.27

In words, if the part being dropped is exactly 5, the last digit kept is
chosen to be an even digit.  This is necessary to avoid a bias toward the
higher number.

    it seems to me that the range  (for example)
    
    	1.2600...  -> 1.26499...  (1.260-1.265, incl. 1.26, excl. 1.265)
    
    is exactly the same size the same size as 
    
    	1.26500... -> 1.26999...  (1.265-1.270, incl. 1.265, excl. 1.27)   	
    
    and so 1.265 should be rounded up to 1.27.
    
    No?
    
    r
    
    
    

re: .49,

Can you provide a reference to this algorithm?  I went
back to a numerical analysis text and could not find
any reference to this algorithm.

Gim

re: .51

>Can you provide a reference to this algorithm? ...

Not without more research than I'm willing to do.

I originally learned this in an RPG programing course.  If my memory is
correct, there is a column on the RPG Calculation specification sheet that
indicates "Half-Adjust" (or maybe just "h"?) -- Ah, in Part II of the 
"Programming in VAX RPG II" manual on page 3-4 column 53 is labled
"Half adjust (H)" -- so my memory appears to be sound!  Unfortunately,
the manual doesn't define "half adjust".

At any rate, I remember the instructor pointing out that virtually all
computer language don't really "round off", but they "half adjust".
Of course, he then had to explain the difference.  Apparently, this
stuck with me.

The reason for this is that the algorithm for half adjusting is very
simple:  (1) Add 5 to the most significant position that is being dropped
and then (2) simply truncate.  Creating an algorithm for rounding is
left as an exercise for the reader.  It will have more steps, and will
involve compare and branch operations.

Now, as a PRACTICAL matter, most people, don't know the difference, or,
if they do, they don't care.  I don't think you'll find this a very
important issue, except in some of the more obscure areas related to
statistical mathematics.

    Have I wasted enough of your time yet???

    Re: .51
    
    Gim, I recollect being taught a similar algorithm in physics
    lab, although probably the direction of rounding 5 alternated,
    in order to avoid introducing experimental bias.
                                  

    	The rounding you are discussing is "round to nearest",
    sometimes referred to as (would you believe?) "Banker's
    rounding".  The short description comes from the IEEE standard
    for Binary Floating-Point Arithmetic (754-1985).  Briefly it
    is: "In this [round to nearest] mode the representable value
    nearest to the infinitely precise result shall be delivered; if
    the two nearest representable values are equally near, the one
    with its least significant bit zero shall be delivered."
    
    	Now, depending upon exactly where that bit falls, this can
    become "round to even", since 15.5 and 16.5 would each become
    16.  It is considered "unbiased", since sometimes it rounds up
    and sometimes down, with equal frequency.  I would point out
    that this is often implemented in computer hardware.  Notice
    that it occurs at the least significant BIT, not digit, so
    the rounding may actually occur at a point you do not expect.
    For normalized numbers, 15.5 and 16.5 have their last bit
    several digits beyond the trailing 5, so rounding would not normally
    take 15.5 or 16.5 to 16.  Actually, it can take quite a bit of work
    to make things round precisely this way in decimal.  Consider that
    6% and 7%, for example, cannot be exactly represented as floating
    point numbers on most binary machines as your starting point.  And
    if you keep them as integers, none of the hardware is there to help
    you with the rounding.  It's really not a simple issue if you happen
    to be a perfectionist...
    
    Cheers!
    Dave Eklund
    

Re .50

>    it seems to me that the range  (for example)
>    
>    	1.2600...  -> 1.26499...  (1.260-1.265, incl. 1.26, excl. 1.265)
>    
>    is exactly the same size the same size as 
>    
>    	1.26500... -> 1.26999...  (1.265-1.270, incl. 1.265, excl. 1.27)   	
>    
>    and so 1.265 should be rounded up to 1.27.
>    
>    No?

No.  Rich, you're artificially setting your ranges here.  1.26 even and 
1.27 even must both be excluded because they aren't rounded -- they already 
*are* the numbers.  And once you've excluded 1.26 and 1.27, including 
1.265 in either half of your range unbalances the other half.
    
Excluding 1.26, 1.265, and 1.27, the 1.26000... -> 1.26499... range is 
exactly the same size as the 1.26500... -> 1.26999... range.  Which is
why, since the 1.265 could go either way, you create a rule so that half
the numbers ending in "5" go one way, and half go the other way.