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In the first sentence, "each week" indicates that Marsha will save $10 every week consistently in order to reach her goal of buying a new bike.
In the second sentence, "each week" is placed after "new bike", which changes the meaning to suggest that Marshall will need to buy a new bike every week in order to reach his goal. This implies a different approach to achieving the goal, as Marshall would need to purchase a new bike weekly rather than saving for a longer period of time to afford one.