S.O.S. Mathematics CyberBoard

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
but have not yet found the correct formula. Please help

/TT

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

_________________
I'm not prejudiced...I hate everybody equally!

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...

_________________
I'm not prejudiced...I hate everybody equally!

[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

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:
http://www.google.ca/search?hl=en&q=800 ... arch&meta=

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

_________________
I'm not prejudiced...I hate everybody equally!

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

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

_________________
I'm not prejudiced...I hate everybody equally!

Thanks - I'll try that

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srgood