To find out how much Naomi saved after a year by not joining the fan club, you can calculate the total cost of joining the fan club for one year and then consider that amount as her savings.
The cost of the fan club is $7.50 per week. There are 52 weeks in a year, so:
\[ \text{Total cost for one year} = 7.50 , \text{(cost per week)} \times 52 , \text{(weeks)} \]
Calculating that:
\[ 7.50 \times 52 = 390 \]
Therefore, by not joining the fan club, Naomi saved $390 after a year.