Take a look and see if you can download XCode.
I'm still very much starting off writing Apps myself but I think Apple has said you need to be designing Apps on the latest of close to the latest version of IOS and some of the older Mac Books do not support newer versions of XCode and therefore do not support newer versions of IOS.
If I had to sum up your question, you probably can write apps on an old mac computer however you may be learning old ways of doing things and you probably wont be able to submit them to the App Store.