Question

I’ve learn that one can easily calculate a monthly or weekly increase or decrease by using the compound interest formula:

A 30 %/year increase:

(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 weekly interest is 0.68 %

A 30 %/year decrease:

(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%

What formula should I use if I have BOTH an increase and a decrease working on the capital at the same time? Performing a “cumulative” calculation where I use the capital value from the week before to calculate the next periods value, yields different results with these formulas. That is, performing the calculations on a weekly basis will yield a different results compared to the monthly calculation. I suppose I need to calculate a new “interest” that takes both the decrease and increase into account? (as using a simple “increase minus decrease” won’t work).

What I want is a report of this type:

week 1: increase-by, decrease-by, capital-size1
week 2: increase-by, decrease-by, capital-size2
...
week 52: increase-by, decrease-by, capital-size52

and

month 1: increase-by, decrease-by, capital-size1
month 2: increase-by, decrease-by, capital-size2
...
month 12: increase-by, decrease-by, capital-size12

Where obviously: capital-size12 = capital-size52

Answer 1

In your examples, for the increase of 30% the capital is multiplied by 1.30 each year, which according to your formula is equivalent to multiplying by 1.0292 per month, or by 1.0068 per week. Similarly for the decreases, the capital is multiplied by 0.70 per year, which is the same as multiplying by 0.9779 per month or by 0.9949 per week. Then to get the weekly or monthly change for a simultaneous increase or decrease, you just need to find the weekly or monthly change corresponding to the product of the annual decrease and the annual increase.

For example, if both changes are by 30% per year, then the net change is 1.30*0.7=0.91 per year, or an annual decrease of 9%. The problem with the particular report you are asking for is that even though the net change per week/month is well defined, the amounts of the increases and decreases depend on whether you apply the increase or the decrease first. If you do simply choose one to apply first, say increase first, then you can add 2.92% to get the increased amount and then subtract 2.21% from the new amount to get the decreased amount, which should be equal to the amount you would find by applying the net weekly/monthly change from the annual 9% change.