Are "despite" and "in spite of" always exchangeable ?
For example, I have such sentences as following.
1. I decided to work out in spite of the rain.
2. I chose to leave this city in spite of the well-paid job.
3. He is quite knowledgeable in spite of his young age.
4. Her living conditions are poor in spite of her high education experience.
5. The elderly man is poorly-paid in spite of the long working hours.

Are these previous sentences correct grammatically in English ? And can I change "in spite of" to "despite" ?
Thank you very much.

Question

Are "despite" and "in spite of" always exchangeable ?
For example, I have such sentences as following.
1. I decided to work out in spite of the rain.
2. I chose to leave this city in spite of the well-paid job.
3. He is quite knowledgeable in spite of his young age.
4. Her living conditions are poor in spite of her high education experience.
5. The elderly man is poorly-paid in spite of the long working hours.

Are these previous sentences correct grammatically in English ? And can I change "in spite of" to "despite" ? 
Thank you very much.

Answer

They mean the same and are interchangeable.  Your sentences are fine and you can substitute despite for the in spite of in all these examples.

Answer

I believe they are interchangeable BUT I do feel that it is more common to use the word 'despite'. I think it's used more often.

I decided to work out, despite the rain.
I chose to leave this city, despite the well paying job.
He is quite knowledgeable, despite his young age.
Her living conditions are poor, despite her high education experiences. 
The elderly man is poorly paid, despite the long working hours.

At least that is how it is in America. I'm not sure of what is more common in other English speaking countries :)