How to use "in spite of"

While I'm doing some exercises in a book. I got a question in which we have to combine two sentences by using "in spite of".

The two sentences are:

I am optimistic about the future. There are so many problems in the world.

My answer was following.

I am optimistic about the future in spite of so many problems in the world.

However, the answer in the book is quite different from mine.

I am optimistic about the future in spite of there being so many problems in the world.

I can understand, the format of the answer in the book. Nevertheless, please someone let me know whether my answer (first sentence) is correct or not.