Renter - page 28
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Oleg, explain your formulas. Write in human language (in general form, not with substituted numbers) the withdrawal formula you used. If you can't write - then I'm not at all sure that you made the program correctly :)
Just don't do it in ASAP language, please. The simpler the better.
If you're not sure... Well... Fine, then... but going around in circles... ten times the same thing...
If you don't want to believe it, I won't try to change your mind...
I have provided all the proofs in this thread.
Recall my formula (initial deposit is conventionally 1, k is withdrawal percentage, q is accrual percentage, t is time in months):
So, withdrawn equals k(1+q) * (1-(1+q-k-qk)^t) / (qk+k-q)
I don't understand, but where did the rest go, MD?
so what are you looking for?
The removed value ?
Or the value of k ?
Your calculations, Oleg, are not up to the level of the problem in my opinion.
I want to make sure that the formulas we use are the same. I will prepare the data tomorrow. But, judging from the last formulas you posted, I really have great doubts that our formulas are the same.
And then we will look for k.
Mathemat:
I don't understand, where did the rest go, MD?
That leaves the forex administration. As our shortfall in profits.
Your deductions, Oleg, are not up to the task in my opinion.
this is the key point...
in your opinion, not up to...
And you admit that your view may be wrong?
Then we will look for k.
Formulate the problem. But without ambiguity, clearly and concisely.
In order to operate with the same input quantities, I will, if necessary, rearrange my formulas so that the comparison of solutions will not cause doubts.
That's why I wrote "in my opinion". Of course I do. Just recently made a mistake with the "material balance", and before that, too, I did not shy away from mistakes... In short, Oleg, I am sorry, I have unfairly attacked you.
Formulate the task. But without ambiguity, clearly and concisely.
The task has already been clearly formulated by the topicstarter, see the first page. By the way, do not understand how you managed to interpret the value of k as a fraction of withdrawal, rather than the percentage. OK, that's sorted out.
The only thing that may be confusing is which value this k refers to. Judging by the first formula derived by Sergei it refers to the deposit at the beginning of the month, i.e. to X. However, the condition says so:
Each month a fixed percentage q of the current deposit amount is deposited. I am allowed to withdraw some percentage k from the account each month, which does not exceed the value of q.
Since withdrawals are obviously made after q has been credited, I propose that the withdrawal not be applied to X, on which q is then credited, but to what is already after q is credited, i.e. to X(1+q) - if the topicstarter agrees. It is on the basis of these assumptions that I decided to revise the formula for withdrawal obtained by Sergei .
The rest seems to be clear. If something is not clear - ask questions, we will clarify it (by the way, I had to think about revising the formula after your question "percentage of what?", and thank you for it).
OK... Never mind...
I'll just draw a picture to make it clear.
actually, it seems logical that k is a fraction of q
since
"to withdraw a certain percentage k from the account each month which does not exceed the value of q"
that's not the point... But...
So.
In the month of January, we have V=100
At B = 100 is charged (30%, that is q = 0.3) - we have in February (1 + 0.3)*B = 1.3 * 100 = 130 = (1 + q)*B
i.e., a surcharge of 0.3*B = 30 = q*B
We remove a part of this surcharge (50%, i.e. k=0.5) k*q*B = 0.5*0.3*100 = 15
As a result for calculation of charges for February we have B=130-15=115
and then
In February we have B=115
. ..... and the same scheme...
That was my reasoning.
What is my mistake?
.
.