If you've ever wanted to know how much longer it'll be until dump, use this formula.

Since we know that the GE goes up max 5% per day, we can use the exponential growth formula to calculate how long it'll take to hit a certain price. This will be helpful if you're wondering how much longer until dump.

Formula:

t=ln(D/C)*20.5
D= Dump price
C= Current price
ln = natural logarithm (this isn't a variable, it's a function on your calculator)
t = time in days

(Note that this is the MINIMUM amount of time it will take. Percent growth varies from 4.5 to 5%)

Derivation:

We start with the compound interest formula, note that I modified the variables: D=C(1+r/n)^(n*t)
D = dump price
C = current price
r = decimal rate of increase (max in GE is 5%, we easily get that, so use .05)
t = time
n = number of times per day GE updates, so 1

So we then plug in the numbers and solve for time:
t= ln(D/C)*20.5

And there you go!

Your money over time:

vertical axis - your money in multiples - 2 would be double your money, 3 is triple, etc
horizontal axis - time in days - overall, this graph covers a month.


Finally, I wanted to make sure everyone knows how to use this, so I'm going to demonstrate.
If our item currently costs 20k and our dump price is 45k, this is what you do:
C=20000
D=45000
t=ln(D/C)*20.5
plug in the numbers and get t=ln(45000/20000)*20.5
Solve it using a calculator or by typing it into google:
t=ln(2.25)*20.5
t=0.810930216*20.5
t=16.6240694 (days)
and you'll always have to round up (even if the result was 16.01 or something like that)
So, minimum possible merch time for this example is 17 days.


Post with your questions/comments.