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 Posted: Fri, 19 Jun 2009 05:40:54 UTC
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Joined: Fri, 19 Jun 2009 05:08:59 UTC
Posts: 10
Hi

I would like to find the formula where you can answer the question:

you start with a one time initial investment (i) of 5000\$ and then you add 1000\$ (d) per month (f) for 8 years (n).

the growth or interest is 7% (g) per year (f2) and the inflation 3%.

this is the parameters i want to use:

Initial investment (a)

deposit per f1 (d) for example 1000 per month

frequency of deposit per year (f1), f1=12 if it is per month

frequency of compound (f2)

interest or growth per year (g)

inflation(i)

years (n)

the calculations are similar to this one, but also includes initial investment.

http://www97.wolframalpha.com/input/?i= ... alue.PMT--

I've come up with an easier version, not including initial investment or f2 (it only works for annual compounding of g).

It looks like this:

(d(1+((g-i)/f)^(fn)-1)/((g-i)/f)

this one is a bit simplified though. I dont know how to do it(Headbang). ive been looking around for instance here:
http://en.wikipedia.org/wiki/Time_value_of_money

/TT

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 Posted: Fri, 19 Jun 2009 19:47:14 UTC
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Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 4091
Location: Ottawa Ontario
Lobotomy wrote:
you start with a one time initial investment (i) of 5000\$ and then you add 1000\$ (d) per month (f) for 8 years (n).

the growth or interest is 7% (g) per year (f2) and the inflation 3%.

It looks like this:

(d(1+((g-i)/f)^(fn)-1)/((g-i)/f)

Hard to tell what you're asking...

Keep it simple: let r = (g - i) / 12 : assuming monthly compounding

P(1 + r)^n + D[(1 + r)^n - 1] / r

That's calculating future value of P (your 5000) plus future value of the monthly deposits D (your 1000).

If 8 years, then n = 12 * 8 = 96

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 Posted: Sat, 20 Jun 2009 20:26:44 UTC
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Joined: Fri, 19 Jun 2009 05:08:59 UTC
Posts: 10
Denis wrote:
Lobotomy wrote:
you start with a one time initial investment (i) of 5000\$ and then you add 1000\$ (d) per month (f) for 8 years (n).

the growth or interest is 7% (g) per year (f2) and the inflation 3%.

It looks like this:

(d(1+((g-i)/f)^(fn)-1)/((g-i)/f)

Hard to tell what you're asking...

Keep it simple: let r = (g - i) / 12 : assuming monthly compounding

P(1 + r)^n + D[(1 + r)^n - 1] / r

That's calculating future value of P (your 5000) plus future value of the monthly deposits D (your 1000).

If 8 years, then n = 12 * 8 = 96

Hi. Are you sure it's correct? I dont think so. I dont think you can just add it like that since starting from P and adding and amount frequently affects the overall interest so it accumulates more.

the above formula is true for if you open 2 accounts with the same interest, one account with an initial deposit and another one that's the regular savings account. this is though not equal to the other

http://www.austenmorris.com/FinanceTools_1.html

using this calculator i dont get the same result with the above formula...

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 Posted: Sun, 21 Jun 2009 04:29:14 UTC
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Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 4091
Location: Ottawa Ontario
Lobotomy wrote:
> Are you sure it's correct?

Yes, I'm sure.

> the above formula is true for if you open 2 accounts with the same interest,
> one account with an initial deposit and another one that's the regular savings
> account. this is though not equal to the other

Makes NO difference; we're looking at ONE account by breaking it
down in 2 parts.

> http://www.austenmorris.com/FinanceTools_1.html
> using this calculator i dont get the same result with the above formula...

I can't comment: I can't see what you're entering!

If you enter 8000 as initial, 1000 as monthly deposit, 96 as n,
and .04/12 as r, you WILL get same results.

8000(1 + .04/12)^96 = 11,011.16

1000[(1 + .04/12)^96 - 1] / (.04/12) = 112,918.53

I've already told you that this what I assumed from the way the problem
is worded; r = .07 - .03 = .04; since monthly, then .04/12

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 Posted: Mon, 22 Jun 2009 02:38:32 UTC
 Member

Joined: Fri, 19 Jun 2009 05:08:59 UTC
Posts: 10
[quote="Denis"][quote="Lobotomy"]
> Are you sure it's correct?

Yes, I'm sure.

> the above formula is true for if you open 2 accounts with the same interest,
> one account with an initial deposit and another one that's the regular savings
> account. this is though not equal to the other

Makes NO difference; we're looking at ONE account by breaking it
down in 2 parts.

> http://www.austenmorris.com/FinanceTools_1.html
> using this calculator i dont get the same result with the above formula...

I can't comment: I can't see what you're entering!

it doesn't matter what you enter since the formula is the same. if you enter your numbers below, the answer is not 11,011.16+12,918.53.... so they are not using your formula at least. you'll get around 123930 while their formula gives 123901

try comparing your calculations to the calculator and you'll see that the answer is different. so appearantly the financial advisors at austen morris would not agree

If you enter 8000 as initial, 1000 as monthly deposit, 96 as n,
and .04/12 as r, you WILL get same results.

8000(1 + .04/12)^96 = 11,011.16

1000[(1 + .04/12)^96 - 1] / (.04/12) = 112,918.53

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 Posted: Mon, 22 Jun 2009 03:49:26 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 4091
Location: Ottawa Ontario
Lobotomy wrote:
...so they are not using your formula at least. you'll get around 123930 while their formula gives 123901

try comparing your calculations to the calculator and you'll see that the answer is different. so appearantly the financial advisors at austen morris would not agree

Once more: 123,930 is correct; Austen Morris' 123,901 is not correct; and the
small difference of 29 only (about 30 cents per month) evidently indicates that
they ARE using the same formula; they must be cheating by rounding down

Here, go see for yourself:

You'll see:
(8 000 * ((1 + (.04 / 12))^96)) + ((1 000 * (((1 + (.04 / 12))^96) - 1)) / (.04 / 12)) = 123 929.697

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 Posted: Sun, 1 Nov 2009 11:55:40 UTC
 S.O.S. Newbie

Joined: Sun, 1 Nov 2009 11:47:22 UTC
Posts: 2
Hi,

From what I can determine, Lobotomy is correct - his formula is for contributions made at the end of each period.

For contributions at the beginning of ea period the formula becomes:

Balance(Y) = P(1 + r)^Y + C(((1 + r) ^(Y + 1) - (1+ r))/r)

My question: how is inflation rolled into these equations? I thought it was a simple adjustment such as "r" becoming "r - inflation%", but in the instance of "r" = "inflation", the equation blows up, since there is division by zero.

Any insight?

thanks.

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srgood

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 Post subject: Posted: Sun, 1 Nov 2009 14:04:49 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 4091
Location: Ottawa Ontario
Nobody said Lobotomy's "formula" wasn't correct.
The problem was in the RATES:
wasn't clear if the 7% was effective annual, or compounded monthly;
the inflation 3% is effective annual.

As far as rate - inflation = 0:
that has a possibility of division by 0 BECAUSE the calculation is combined;
but there really is 2 calculations:
one using interest rate, one using inflation rate;
both will result in same, thus zero.

Furthermore, 7% cpd monthly cannot be combined with 3% cpd annually
as .07/12 and .03/12; the .03 needs to be adjusted in this manner:
(1 + x)^12 = 1.03

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 Posted: Mon, 2 Nov 2009 00:15:10 UTC
 S.O.S. Newbie

Joined: Sun, 1 Nov 2009 11:47:22 UTC
Posts: 2
Thanks - I'll try that

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srgood

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 Posted: Sat, 30 Nov 2013 08:58:54 UTC
 S.O.S. Newbie

Joined: Sat, 30 Nov 2013 08:57:29 UTC
Posts: 1
There's been a ton of discussion about how Americans do not save enough cash. While it is certainly true that frivolous spending is bad, what a lot of people don't understand that they really lose money if they save it. The reason has to do with inflation, which makes most savings accounts almost pointless to have. How often have you wanted additional information on the best wayshort terms loans, and resorted to an internet search on emergency payday cash loans.

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 Posted: Sat, 30 Nov 2013 09:55:16 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 4091
Location: Ottawa Ontario
Arnold, go play in the traffic at rush hour...
not ok to save, but ok to be in a position to require payday loans?!

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