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Any help on this is much appreciated!

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- Apr 9th 2008, 04:58 AMcirrus74Finance/Actuarial question. Please help!
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Any help on this is much appreciated! - Apr 9th 2008, 06:01 AMkalagota
i'll use to denote the accumulated value of the annuity since i dont know the code in LaTex..

so,

and assuming that this is a compound interest, then we can use

therefore, the middle part can be simplified (evaluated at ) as (verify) and together with the right hand side, we have or

therefore, - Apr 9th 2008, 06:09 AMcolby2152
Please do not double post. You question was first answered in the Business Math forum: http://www.mathhelpforum.com/math-he...-function.html

- Apr 9th 2008, 06:10 AMTKHunny
You should have these:

Let's see what you get.

Note: I'm not sure what Kalagota is missing. It doesn't make sense for 10 payments to be accumulated to only 8½, so you get to tell us what you manage to calulate. - Apr 9th 2008, 07:22 AMkalagota
now i wonder what i missed? (Wondering)

i think, my mistake was that thing.. i forgot that the integral was a power of and thus, should be equal to .. this should make sense... (Rofl)

now, let me correct my mistake..

or

thus, - Apr 9th 2008, 07:44 AMTKHunny
Try again. I'm holding out for 14.5. (Yes)

- Apr 9th 2008, 07:55 AMkalagota
how you did yours?

is ? it can't be i think, and i shall stick with .. - Apr 9th 2008, 08:56 AMTKHunny
Formulas shown above. I think yours is missing some moving parts.

Start from , rather than the summed version that assumes regularity of interest for each payment.

With variable interest, . - Apr 9th 2008, 02:43 PMcirrus74
- Apr 9th 2008, 04:17 PMTKHunny
The integral is good. You will need that.

Look at my first post very carefully. There is a summation in there. If you are trying to do it in one piece, you do not yet have the right idea. - Apr 9th 2008, 07:49 PMkalagota
did you notice notice that your summation is just the sum of the first n geometric sequence.. i think, you must be the one to check your solution.. or the best way is to post your whole solution in here..

besides, if you will push your 14.5, try to work it backward, and you will derive at and not 2.. - Apr 9th 2008, 08:23 PMkalagota
maybe i'll put the derivation here..

thus,

or

and

and just do your substitution.. - Apr 10th 2008, 12:31 AMcirrus74
Thanks, I've got the answer. Do you mind if I ask a question though?

Why can I not just use this? Or at least, the answer doesn't turn out right, but I don't understand why.

exp(-ln(20 - 10)+ ln(20-1)) = exp (ln(19/10)) = 19/10

Did I make a mistake somewhere? - Apr 10th 2008, 10:37 AMTKHunny
- Apr 10th 2008, 11:06 AMTKHunny
Another Possible Answer:

As it stands, we have 't' defined as the time from EACH deposit. That may not seem quite right. If we use 't' to mean the time from the beginning of the financial structure, we get:

Then:

Very interestingly, we get:

s(0) = 2.00

s(1) = 1.90

s(2) = 1.80

etc...

It IS an arithmetic sequence.