No, it won't work. Look at this page:
http://www.modthesims.info/wiki.php...em_Requirements
The Geforce 8400 GS is flagged as "No" across all the Sims 3 games. Plus, at the bottom of the table, it says: "At least some if not all of Nvidia's cards with G86 and G84 cores are defective. They they do not handle heat like they should. This includes all GeForce 8400/8500/8600/8700 cards."
Be careful what you buy. With computer cards, you really get what you pay for, and I highly doubt you will find a suitable card for such a low price. You also have to take into account the other parts of your computer, to see if the new card would be compatible with them.
Someone else might offer more/better advice regarding how to choose a good card.