In order to answer your question, you need to model more precisely your domain:
- If you just compare the daily balance of the account, you will find a 110% increase. But that's not a profit, it's a variation.
- If you do not have precise definitions, you might also consider that the profit is only 5% at the end of the second day, since the use made $200 deposits in total and the only profit made with this money in the two days is $10.
To make meaningful financial analysis, you need to know the movements that happened on your account and justify the changes in the account balance:
- profit: additional money earned, that the customer didn't own before
- loss: money lost, that the customer does no longer owns
- transfers, such as deposits and withdrawals, i.e. money that was and is still owned by the customer but may or may no longer be on the account.
The profit and loss analysis makes only sense for a well defined period:
- If you have a profit of $10 on first day of the month, and an additional profit of $20 on the last day of the month, your profit for the month is $30.
- If you're analysing the daily profits and loss, the daily profit of the last day of the month is only $20, because the $10 earned on the first day of the month are already owned by the customer on the second day.
Note also that profit and loss are understood as the net result of one or several transactions. In reality it is the result of the revenue minus the expenditures. So if your interest is $10, but the bank charges a fee of $1, $10 would be the income, $1 the expenditures and $9 the profit.