Excellent. Thank you for taking the time to respond. I appreciate it.


"Mark Freeland" <nBeOwXs[at]pacbell.net> wrote in message
news:4149CB56.795A[at]pacbell.net...
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======================================= MODERATOR'S COMMENT:
Please trim the post to which you are responding.

BMS wrote:
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Strater is only contributing 1,000 per year. So you are correct that
this will give the future value, but one still needs to work backward to
get the effective annual rate for the base amount of $1,000.

Curiously, your analogy to an annuity is apt - some annuities offer a
"bonus" yield the first year or so, which is in effect what a company
does when it matches the contribution. But for annuities, the "bonus"
is typically 1% to 5%.
http://www.sec.gov/answers/bonuscredits.htm

See below for calculation:

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It makes perfect sense.

Let's assume that the company is matching w% (forget about x for now),
say the company matches 50% (w = 50).

Let's further assume that the average rate of return of the investment
(forget about whether it was matched or not) is r%/year, say 10%, so
that a dollar invested is worth $(1+r/100) after one year.

You contribute C dollars (say $1000). The company matches w%, so your C
dollars starts you off with C * (1+w/100) dollars.

After 1 year, this is worth C * (1+w/100) * (1+r/100).
After 2 years, this is worth C * (1+w/100) * (1+r/100) * (1+ r/100).

You get the idea.
After z years, this is worth C * (1+w/100) * (1 + r/100) ^ z.

This is the result (future value) that BMS was referring to. But you
still need to work backward to get the effective annual rate.

After z years, you have multiplied your initial investment, C, by
(1+w/100) * (1+r/100) ^ z.

This is the same as multiplying your initial investment C, each year, by
[(1 + w/100) * (1 + r/100)^z] ^ (1/z) =
[(1 + w/100) ^ (1/z)] * (1 + r/100)

Subtract 1, and you have the average annual rate of return.

For example, with 50% match, 10% return, and 10 years, you have:
[(1 + 50/100) ^ (1/10)] * (1 + 10/100) - 1 =
(1.5 ^ 0.1) * 1.1 - 1 =
1.04138 * 1.1 - 1 = 0.1455, or 14.55%.

Checking:
$1000 * (1+14.55%) ^ 10 = $3891 (using effective rate)
($1,000 + $500) * (1+10%) ^ 10 = $3891 (using real rate + match)

Finally, what to do about the cap on the matching (x)? Just adjust the
matching percentage:

If you contribute <= x%, then use w% as the matching rate.

If you contribute > x%, then the number of dollars matched is fixed, at
some M = wages * x% * w%; the percentage of match is M/C (where C is the
amount you contributed). Use that value for w in everything above.

--
Mark Freeland
nBeOwXs[at]pacbell.net

The math you want to use is the same as an annuity. You are contributing
1500 per year, say for the calculator it's ten years. Then using your
compounding rate to get the future value.
...

"Strater" <jstrater[at]dev.logiq.net> wrote in message
news:ci55ei$n0d[at]library2.airnews.net...
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I frequently see posts touting a company match of X% on a 401k as equivalent
to a guaranteed return on your investment of X%.

I have been trying to figure out a formula of the effect of a company match
in terms of compound interest percentage yield, and I realized that I am
confused. Because of compounding, I don't think I am comparing apples to
apples.

For example, if I make $10,000/year, and I contribute 10% to my 401k, and my
company matches 50% of that:

10,000 x .10 = 1,000
1,000 x .50 = 500

Total = 1500

This is a 50% return.

After 10 years I would have $15,000 for my initial $10,000 investment.
Again, a 50% return. No argument there.

However, this is not the same as a investing in a mutual fund that returns
50% per year, where an initial $10,000 investment compounded for 10 years at
50% would be over $1 million.

Probably obvious to everyone but me.

Okay, given all that, does anyone know of a formula that does equate company
match to compound interest yield?

What I'm getting at is this: Having a company match of w% up to your first
x% is as good as getting an extra y% in compound interest rate over z years.

Or does that not even make any sense?