How to sync apps with new iPhone 3GS?

mets819

New member
Ok so I recently bought a new iMac and upgraded from my iPhone 3G to the 3GS. Since I no longer have my old computer or iPhone will I have to rebuy all my apps or are the apps linked to my itunes account. If they are linked to my account when I set up itunes on my new iMac will i be able to redownload them all and sync them to my 3GS for free.
Thanks.
 
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