Compound interest but with a twist: "compound tax"

Let's say that I have a diminishing value that should be portra开发者_如何学Cyed 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:

(1+x)^12 - 1 =30% then x=0.0221  the monthly interest is 2.21%
(1+x)^52 - 1 = 30% then x=0.0051 the weekly interest is 0.51%

But what you should have done is:

(1-x)^12=1-30% then x =0.0292 the monthly interest is 2.92%
(1-x)^52=1-30% then x=0.0068 the monthly interest is 0.68 %

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 .

Engaging psychic debugging...

diminishes by 30 %/year. Which when I calculate (by normal "periodic compound" formulas) is 2.21 %/month and 0.51 %/week.

You are doing an inappropriate calculation.

You are correct in saying that 30% annual growth is approx 2.21% monthly growth. The reason for this is because 30% annual growth is expressed as multiplication by 1.30 (since 100% + 30% = 130%, or 1.30), and making this monthly is:

1.30 ^ (1/12) = 1.0221 (approx)

However, it does not follow from this that 30% annual shrinkage is approx 2.21% monthly shrinkage. To work out the monthly shrinkage we must note that 30% shrinkage is multiplication by 0.70 (since 100% - 30% = 70%, or 0.70), and make this monthly in the same way:

0.70 ^ (1/12) = 0.9707 (approx)

Multiplication by 0.9707 is monthly shrinkage of 2.929% (approx).

Hopefully this will give you the tools you need to correct your calculations.