I am studying calculus and I recently thought up an interesting problem that I cannot solve. A little context - I have invested in Bitshares, a cryptocurrency that enables you to "borrow" an asset by underwriting the value of the asset with your own balance of Bitshares. For example, if one Bitshare is worth 1USD and I have 4 Bitshares, I can "borrow" 2USD by locking up my 4 Bitshares as collateral. I can then sell this USD Asset - if the value of Bitshares goes up then I can remove some of the collateral, but if the value of Bitshares goes down I must settle my debt, add more Bitshares to the collateral or risk my position being automatically closed.

So, if I use my account balance to "borrow" +20% on top of my deposits, and Bitshares goes up in value at a constant rate (say 10% a month), how long would it take for my Bitshares balance to increase from 100,000 Bitshares to 1,000,000 Bitshares?

I found this a complicated question to answer because as Bitshares goes up in value a number of Bitshares generated from the short position (borrowing USD and then selling it for Bitshares is effectively shorting USD against Bitshares) diminishes while as the account balance of Bitshares increases the amount of USD 20% "borrows" increases.

I find it easy to work through the problems in my calculus course (maybe easy is not the right word), but I get lost on real world problems.

We can make assumptions about the price of Bitshares, but currently, it is about $0.09.


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