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Is it making the noise all the time? only in turns? only when you coast? or only on accel?
The cost will depend on what the problem is. Just need a little more info
You may want to go to a doctor, grinding isn't right.
For the rear axle, Grinding is most likely a gear out place or low on fluid. You could have a bad bearing that is letting the gears out of mesh or a overtorqued crush collar or failed gears. An axle rebuild should be $1200-2000 depending on what you put back in (ie locking or LS diff, which gears, all new bearings, fancy diff cover, expensive fluid). A new axle is probably $2-3k and a used one something like $1500-2k.