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In spite of the fact that Vronsky seems like this young guy about town, he's actually really particular about keeping his accounts in order.
When he was young, he tried to get a loan and got refused and the humiliation has made him totally serious about keeping himself financially squared away.
In keeping with this hidden nature, Vronsky does his accounts from top to bottom five times a year.
This is one of those days, and we get a detailed summary of his financial situation.
It turns out that Vronsky is not as wealthy as he would like to be. His mother has been withholding money due to her displeasure over his affair with Anna. In her last letter, she essentially tried to bribe him into giving up the affair. He refuses, writing a short, sharp letter to his mother, and instead resolves to borrow ten thousand from a moneylender, to cut down his expenses, and to sell his racehorses to cover all of his bills.