NY Money Achievements and Banking Fees

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When I finally got 10 Trillion dollars of NY currency outside of the bank, I couldn't wait to get my Nest Egg Achievement Badge.   I knew if I deposited the 10 Trillion dollars, I would be disappointed because the badge clearly states the this amount is after the bank fees.
(click on any image to enlarge)

I knew the extra money needed for the fees would also be have fees so I asked my mafia if anybody knew the exact number.  The easiest way for me to get answers to my questions is to ask my mafia.  I made the following post and learned I needed to deposit $10,752,688,172,044.

It was important for me to mention that I had vaulted the Money Laundering Collection because the bank deposit fees are reduced by 3%.  When dealing with trillions of dollars, 10% vs 7% is a significant amount of money.  If you haven't vaulted this collection yet, you really should.  These items are readily available and if you ask your mafia members, it should be hard to get all of them.

Many of my mathematically inclined mafia members came out of the woodwork and not only did I get the answer I was looking for but I got some detailed information as well.  Tom Hughes provided the following equation to help me understand
Reasoning: the 7% "fee" is actually a 0.93 multiplicative factor, so dividing by that factor cancels the factor (by the general rules of algebra).
Example: You have to have $10,000,000,000,000 to get the achievement.... In order to deposit that amount, you need $10,752,688,172,044. The 7% "fee" is the same as multiplying your total by 0.93. Multiplying $10,752,688,172,044 by 0.93 yields exactly $10,000,000,000,000, which is the value required for that achievement.
Formula:  The formula for this transformation is as follows: 
Y = Amount remaining after deposit
X = Amount of cash on hand prior to deposit
X = Y/(0.93)

Mathematics: 

($10,000,000,000,000)/(0.93) = $10,752,688,172,044;

Reversing the order:

($10,752,688,172,044) * (0.93) = $10,000,000,000,000

Peggy McIntyre who is the Lead Administrator for [♥ஜ♥ THX ♥ஜ♥]® tested this out by depositing $10,752,688,172,044 into the bank and took screen shots before and after.

Forgetting to turn off the banking feature of The Brawler bookmarklet set me back a few days but eventually I got all the money I needed and made the deposit.

I could have just checked the The Mafia Wars Wiki Achievement Page but I wanted somebody to explain to me where this number came from.  Here are all 4 of the NY money achievements.  We only need to worry about the bank fees for the first 3.  As far as getting the "What's After Trillion?" Achievement Badge, read my article titled What's After Trillion for a strategy on that.  I now have 989 Trillion dollars to go!
(image created from images on the Mafia Wars Wiki Achievement Page)