Renter - page 5
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We can't swallow the idealised condition here yet. Let alone find a solution to the problem. And you, Sorento, about inflation...
Without inflation and minimum consumption amount, the best solution would be to withdraw all interest at the end of the period. The formal solution is in the book I posted on the last page. It's pretty clear as it is. The solution for inflation and necessary consumption is also there.
Sorry, Lord_Shadows, I seem to be getting knocked out by Jurin's communication style. I'll have a look.
So, look, again you didn't specify in the condition that we won't get this interest q for period t, except for the monthly withdrawal of interest k. Man, this changes the whole problem altogether.
Without regard to inflation and minimum consumption amount, the best solution is to withdraw all interest at the end of the period. The formal solution is in the book I posted on the last page. It's pretty clear. The solution for inflation and necessary consumption is also there.
What about the optimum for k (share of withdrawals), which is clearly visible in the graphs for the case without inflation and without taking into account the minimum amount of consumption?
Or is that not a fact?
Lord_Shadows:
OK, look, again you didn't specify in the condition that we will not obtain this interest q in period t, except for the monthly withdrawal of percentage k. Man, that changes the whole problem altogether.
The wording of the problem:
Parameters:
a. Initial deposit.
b. Monthly interest rate.
c. The amount needed per month.
Variable:
d. Once in how many months to make a withdrawal.
Find:
d at which the sum of the remaining funds on deposit plus the sum of all withdrawals is maximum.
d at which the sum of the remaining funds on deposit plus the sum of all withdrawals is the maximum.
The wording of the task:
Integer, this is a different problem. For her, the answer is obvious: You should not withdraw before the end of the period. In this case, the amount withdrawn plus the deposit is the maximum.
Let's talk about the topic of the topic. I have a more interesting problem (if you think about it).
then Reshetov is right.
Reshetov is right if periodic withdrawals are not necessary. In this case, it is.
What about the optimum for k (share of withdrawals), which is clearly visible in the graphs for the case without inflation and without taking into account the minimum amount of consumption?
Or is it not a fact?
That's how I am.got it wrong somewhere. Any withdrawal before the end of the period reduces the final amount, as the amount withdrawn would have brought income for the remaining time.
Integer, that's another task. For her, the answer is obvious: You should not withdraw before the end of the period. In this case, the amount withdrawn plus the deposit is the maximum.
Let's talk about the topic of the topic. I have a more interesting setting (if you think about it).
If you have to withdraw at least C, then the best solution is to withdraw C every time (i.e. the minimum). The problem has a different solution when inflation is taken into account (or more precisely, when inflation may be higher than the interest rate)
got it wrong somewhere. Any withdrawal before the end of the period reduces the final amount, as the amount withdrawn would have brought income for the remaining time.
No, no. Not wrong. Here is the dependency of the withdrawal amount, which follows from the iterative formula (in red), and from the analytical dependency (in blue).
It can be seen that they coincide and there is a maximum by k (on the previous page of the topic).