Renter - page 7

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I've come to the point where I need a formula for the sum of a power series :(

Do I need this general solution, if the answer is a single digit which does not depend on any conditions? Write a program and let an iron machine do the work.

 
Integer:

I've come to the point where I need a formula for the sum of a power series :(


Well, it's kind of a non-issue! Draw a general view of a power series.

 

The formula for the withdrawable profit for each month:

fp = (d * (1 + pp) ^ (m - 1)) * ps

d is the initial deposit.

The bank rate (ratio) is pp+ps. pp - we keep it, ps - we withdraw it. At first we make the deposit (pp+ps), and then we withdraw part of it (ps), and keep the other part (pp). Maybe it would be better to enter withdrawal coefficient from the accrued, then in the formula will be bank interest and withdrawal coefficient from the accrued).

m is the number of the month.

 
Neutron:

Sergei,

I suggest you supplement the problem with the inflation rate, i.e. withdraw the maximum possible k = q - inflation. (i.e. the deposit remains not less than the initial amount in real terms / naturally, for simplicity we consider inflation as a constant value/).

I wonder how much the solution will change.

 
alsu:



Alexei, what difference does it make?

Let the monthly inflation rate be I per cent. Then, for the equation of the withdrawal amount for period t , we can write:

For the derivative of k: i.e. by replacing the variables q-I by Q we automatically come to the same expressions as above and hence we will not make our life easier in terms of obtaining an analytical solution for df/dk=0.

So what did you mean by that? Simply adding an additional term responsible for inflation to the expression? It is certainly interesting, but it's not the best way to complicate the model without the solution of the simplest scenario.

Integer:

The formula of profit withdrawal for each month:

fp = (d * (1 + pp) ^ (m - 1)) * ps

d is the initial deposit.

The bank rate (ratio) is pp+ps. pp - we keep it, ps - we withdraw it. We start with pp+ps, then withdraw (ps) and keep (pp). Maybe it would be better to enter withdrawal coefficient from the accrued, then in the formula will be bank interest and withdrawal coefficient from the accrued).

m - sequence number of the month.

Integer, is your fp and my f the same thing? If so, why do you not have 1 in the numerator, which is taken from the sum of a power series, and why do you not have a denominator, which is taken from the same.

 

First, let's look at the filling of the first vessel only -- the second vessel is off, the valve is closed -- there is no withdrawal from the deposit.

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and remember that for the discrete version used the growth factor = 0.2

well these are subtleties...

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on the second step let's open the valve ;)

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zy.

here we will not introduce a lag - in order not to complicate things

 

I think it is useful to remember the annuity formula and how it is derived...

;)

 
annuity -- I've always liked such fun words :)))
 
Sorento:

I think it is useful to remember the annuity formula and how it is derived...

;)

It was derived by bankers in order to extort more interest from clients under the guise of taking care of them...)
 

Well, bankers are not in the clear!

so this annuity explains how to turn on the valve?

:)))

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