Permission Error When Trying To Install Rails (OSX)

I am new to programming and am trying to get rails installed on my terminal. I have been following instructions from a friend, installing the xcode command line tools, homebrew, git, rbenv, ruby-build, ruby gems, ruby, and postgres. But whenever, I try $gem install rails, I get the following:

Russell-Silvers-MacBook-Pro:~ Russell_Silver$ gem install rails
ERROR:  While executing gem ... (Errno::EACCES)
    Permission denied @ rb_sysopen - /Users/Russell_Silver/.rbenv/versions/2.1.5/lib/ruby/gems/2.1.0/gems/rails-4.2.0/README.md

This is especially frustrating because when I run $gem list, it says I have rails 3.2.18. Which is peculiar, because when I run $rails v$, it tells me I have Rails 4.2.0.

When I try to use rails rails my new_app

Errno::EACCES: Permission denied @ rb_sysopen - /Users/Russell_Silver/.rbenv/versions/2.1.5/lib/ruby/gems/2.1.0/gems/rails-4.2.0/README.md
An error occurred while installing rails (4.2.0), and Bundler cannot continue.
Make sure that `gem install rails -v '4.2.0'` succeeds before bundling.
         run  bundle exec spring binstub --all
/Users/Russell_Silver/.rbenv/versions/2.1.5/lib/ruby/gems/2.1.0/gems/bundler-1.8.3/lib/bundler/shared_helpers.rb:83: warning: Insecure world writable dir /Users/Russell_Silver in PATH, mode 040707
bundler: command not found: spring
Install missing gem executables with `bundle install`
Russell-Silvers-MacBook-Pro:~ Russell_Silver$ bundle install
/Users/Russell_Silver/.rbenv/versions/2.1.5/lib/ruby/gems/2.1.0/gems/bundler-1.8.3/lib/bundler/vendor/thor/shell/basic.rb:355: warning: Insecure world writable dir /Users/Russell_Silver in PATH, mode 040707
Could not locate Gemfile or .bundle/ directory

This is really frustrating, especially for someone new to programming such as myself, so I am seeking help from anybody who might know what is wrong.