How can economies grow if every account is perfectly balanced against others? In an economy with finite actors, if every account is perfectly balanced against another account, how can the economy grow when new money enters?  I am thinking of the following chain of events:


The Fed prints money
   + Fed: $+$ debit (imbalanced book)
A Bank recieves cash from one of the 12 regional Fed banks


Fed: $-$ credit (balanced book)
Bank: $+$ debit (imbalanced book)

Lady takes loan out from the Bank


Bank: $-$ credit (balanced book)
Lady: $+$ debit (imbalanced book)

Lady is payed by her company


Lady: $-$ credit (balanced book)
Company: $+$ debit (imbalanced book)

People buy good or service from company


Company: $-$ credit (balanced book)
People: $-$ debit (imbalanced book)



And from here I am too confused to continue $\dots$ I am not sure we can say credit and debit in this sense, I just mean to show there is someplace that is always unbalanced.  The conclusion I always end up with is that this chain is complete (all parties are balanced) when a new loan is taken out, .. but this makes another chain, which I feel just cannot be the answer!
The Accounting mistake is in step 1, obviously, since you performed a single-entry and not a double-entry:
The Central Bank books are not imbalanced: schematically speaking the CB credits the account "money creation" (or "Our future") and debits its own "Cash Available": this is the essence of "the printing privilege": the CB has the right to create money out of thin air.
Then, it credits its Cash Available account and debits the customer/borrower "Commercial Bank" -because Commercial Bank don't just get money from the Central Bank, they borrow it (or the Central Bank instead of lending money, it buys shareholder stock of the commercial bank or any other so-called "open market operations"). 

So all books balance. As regards growth in such a balanced-book situation, the key is in step 5, "People buy good or service from company": 

What tells you that the firm has the capacity to serve the demand it faces? If demand is now increased because new money have flown into the economy (and initially people treat money as a store of value/purchasing power, not just as a medium of exchange in a static situation), the firm may have to increase its productive capacity to satisfy total demand.

If it cannot do that, the firm will see an opportunity to raise prices, hence new money will just cause inflation. But if the firm can increase its productive capacity, namely, if there is people unemployed and capital laying idle, then the firm will "call to arms" these currently unemployed factors of production, and it will put them to work and produce, thus increasing output and so creating growth.

This effect can certainly be written using the balanced-book Accounting Language, but I will leave that as an exercise.