If the fan club costs $7.50 a week, we can calculate the yearly cost and the amount Naomi saved by not joining.
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Calculate the weekly cost: \[ \text{Weekly Cost} = 7.50 \]
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Calculate the yearly cost: \[ \text{Yearly Cost} = \text{Weekly Cost} \times 52 = 7.50 \times 52 = 390 \]
So, by deciding not to join the fan club, Naomi saved $390 after a year.