Talk:Achievements/@comment-2144330-20100701122627

What's after Trillion? achievement

It is a big mistake to upgrade properties as much as you can because after certain number these become counter productive. Do not upgrade more than 100 lvl per each property.

Key for this achievement is a Agostino Cleto Boss fight under Enforcer tiar, and here is my math homework ;)

Mt - stands for Money Target. For those with 10% fee Mt=1098900000000000 and for those with 7%, Mt= 1068930000000000

Mc - stand for amount of starting cache (money you currently have)

From each fight you will earn 1/555 part of money you currently have (NOT INCLUDING YOUR MONEY ON BANK ACCOUNT). So after first fight you will have:

Mc(1) = Mc + Mc / 555 = Mc * (1 + 1 / 555) = Mc * 1.0018

...after second fight:

Mc(2) = Mc(1) * 1.0018 = Mc * 1.0018 * 1.0018 = Mc * 1.0018^2

...after third fight:

Mc(3) = Mc * 1.0018^3

...and after n fights:

Mc(n) = Mc * 1.0018^n

...where n represent a number of needed Boss fights to achieve Mt. As we can see, 1.0018 is a constant and I will name it as C.

Further we have:

C = 1.0018

ln - natural logarithm

Mt = Mc(n) Mt = Mc * C^n Mt / Mc = C^n n = log(C)(Mt/Mc) n = ln(Mt / Mc) / ln(C) n = [ln(Mt) - ln(Mc)] / ln(C)

In 7% fee case we will have:

n=[34.6054 - ln(Mc)] / 0.0018

In 10% fee case we will have:

n=[34.6330 - ln(Mc)] / 0.0018

For example, i have $492,632,377,364 now so this is my Mc and my bank fee is a 7%. After using math formula, number of Boss fights until reaching achievement will be:

n=[34.6054 - ln(492632377364)] / 0.0018

n=4267

I can do a Boss fight 10 times per day so, I will reach this achievement in 426,7 days or about 14 months AND ONLY FROM BOSS FIGHTS. If you add money from jobs, robbing, fights... period will be shorter.