(Note: You should do Part I first before doing this.)

After Sylvia moves 40% of her saving to Sylvatra's bank account, Sylvia and Sylvanna make a competition for 2 years. Sylvia saves $42 every 3 months, while Sylvanna saves $49 every 4 months. In the end of the first year, the one who have more saving should give \(\frac {1}{7}\) of her saving into the other's account. In the end of the second year, the one who have more saving will win. Who will win the competition and how much money will she have?

Details and Assumptions: In the end of the first and second year, they count their saving after they save the money.

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