Walmart offers the Trademark Home 38" Magnetic Screen Door, model no. 82-18PM, for $7.88. (Amazon charges the same with free shipping for Prime members.) Choose in-store pickup to avoid the $4.97 shipping charge. That's the lowest price we could find by $7, although we saw it for a buck less in August. It features 18 magnets and measures 38" x 80".
Update: 13 Deals offers one that measures 83" x 19.5" for $7.49 with free shipping.