My Mutual Fund Questions(s), Solved??

[Crackles McFarly]

Following scenario
$1,000 invested
6% rate annually
$100 per month [$1,200 for a year]
Total Time invested = 1 Year [12 months]
The Results vary, a lot.

FV in Excel Says $2,301.40
http://www.planningtips.com/cgi-bin/savings.pl
Said = $2,295.23
http://www.abgnational.com/calculators/CompoundSavings.html
Said = $2,299
http://personal.fidelity.com/toolbox/growth/growth.shtml
Said = $2,332
http://www.csgnetwork.com/compoundint2calc.html
Said = $2,332
http://www.finance.cch.com/sohoApplets/InvestmentReturn.asp
Said = $2,312
http://www.americancentury.com/workshop/time_value_calc.jsp
Said = $2,301


http://www.moneychimp.com/calculator/compound_interest_calculator.htm
LOOK = 2,301.40 <--Same as FV


I think this is because of the compounding issue. Some of these
calculators compounded annually by default, some did it by default and
didn't allow you to change it.

It's the compounding stupid!

Mind you, these are a snapshot of the online calc websites. I'm sure a
few thousand more exists.

I'm in hopes I figured this out finally?

 

[Harlan Grove]

Following scenario
$1,000 invested
6% rate annually
$100 per month [$1,200 for a year]
Total Time invested = 1 Year [12 months]
The Results vary, a lot.

Terminology and rounding are killers!


First principles.


6% effective annual interest

Accumulated value of the initial 1,000 investment at the end of the year,
that is as of the end of the 12th month,

FV1 = 1000 * 1.06 = 1060

Accumulated value of the 12 monthly payments at the end of the 12th month,
which means the last 100 monthly additional deposit earns no interest,

FV2 = 100 * 6% / (1.06 ^ (1/12) - 1) = 1232.65

Total accumulated value is just the sum of the two pieces.

FV = FV1 + FV2 = 2292.65


6% nominal compounded monthly

FV1 = 1000 * 1.005 ^ 12 = 1061.68

FV2 = 100 * (1.005 ^ 12 - 1) / 0.005 = 2295.23


Both assume intermediate calculations are stored in at IEEE double
precision, which is NOT necessarily the case with some common scripting
languages or Java.

Now assume the 100 additional deposits were treated as made at the beginning
of each period, so the total deposit at the beginning of the 1st month were
1,100.

Effective: FV2 = 1238.65 and FV = 2298.65

Nominal: FV2 = 1239.72 and FV = 2301.40

FV in Excel Says $2,301.40

In which case your formula must have been

=FV(6%/12,12,-100,-1000,1)

So nominal compounded monthly with deposits made at the beginning of each
month, so the total deposit made at the beginning of the 1st month is 1100.

http://www.planningtips.com/cgi-bin/savings.pl
Said = $2,295.23

Nominal compounded monthly with additional deposits made at the END of each
month, so the last deposit accrues no interest. Excel would give the same
result with

=FV(6%/12,12,-100,-1000,0)

[Figures Perl programmers would get this right.]

http://www.abgnational.com/calculators/CompoundSavings.html
Said = $2,299

Effective annual with deposits made at the beginning of each month, rounded.

http://personal.fidelity.com/toolbox/growth/growth.shtml
Said = $2,332
http://www.csgnetwork.com/compoundint2calc.html
Said = $2,332
http://www.finance.cch.com/sohoApplets/InvestmentReturn.asp
Said = $2,312

These are fubar.

http://www.americancentury.com/workshop/time_value_calc.jsp
Said = $2,301

Nominal compounded monthly with deposits made at the beginning of each month
but rounded.

http://www.moneychimp.com/calculator/compound_interest_calculator.htm
LOOK = 2,301.40 <--Same as FV

Nominal compounded monthly with deposits made at the beginning of each
month.

I think this is because of the compounding issue. Some of these
calculators compounded annually by default, some did it by default and
didn't allow you to change it.

No, they don't compound annually. They compound monthly BUT at the effective
annual rate, 1.06^(1/12)-1 = 0.486755056534305% rather than 0.5%.

It's the compounding stupid!

....

And when deposits are made.