Let’s say that I have a diminishing value that should be portrayed both on a monthly basis and on a weekly basis.
For example. I know that the value, say 100 000, diminishes by 30 %/year. Which when I calculate (by normal “periodic compound” formulas) is 2.21 %/month and 0.51 %/week.
However, looking at the results from these calculations (calculating for a entire year) I do not get the same end valued. Only if I calculate it as a “interest” (=the percentage is ADDED to the value, NOT taken away) do I get matching values on both the weekly and monthly calculations.
What is the correct formula for calculating this “compound taxation” problem?
I don’t know if I fully understand your question.
You cannot calculate diminushing interest the way you do it.
If your value (100 000) diminishes by 30 %/ year this means that at the end of year 1 your value is 70 000.
The way you calculated you compound would work if diminishing by 30% meant 100000/1.3
Your mistake:
You made your calculation this way:
But what you should have done is:
You cannot calculate the compound interest as if it was increasing 30% when it’s decreasing 30%.
It’s easy to understand that the compound interest for an increasing will be smallest than the one for decreasing:
Exemple:
Let’s say your investment makes 30% per year.
At the end of first month you will have more money, and therefore you’re investing more so you need a smaller return to make as much money as in the first month.
Therefore for increasing interest the coumpond interest i=2.21 is smaller than 30/12 = 2.5
same reasonning for the decreasing i =2.92 > 30/12=2.5
note:
(1+x)^12 – 1 =30% is not equivalent to (1-x)^12=1-30%
negative interest cannot be treated as negative interest:
following what you did adding 10% to one then taking away 10% to the result would return one:
(1+10%)/(1+10%)=1
The way it’s calculated won’t give the same result : (1+10%)*(1-10%)=0.99
Hope I understood your question and it helps .