This is 100% a scam. This person was not working for Microsoft and Microsoft would never call you for no reason.
This is what is known as "phishing" it is can be a very serious problem if you do let them access your computer.
Basically what they will do is create fake websites and say that you have problems. Any actual computer problems you have will be entirely coincidental. Usually what they will do is show you the windows error log which always shows a lot of errors but these are normal and on all windows computers, they are not viruses.
Next they log onto your computer and lie to you about the numerous problems they pretend to find. Next they will attempt to get you to pay a few hundred dollars to "fix" the issues when in fact they actually do nothing.
Sometimes they lock people out of their systems and steal their credit cards as well.
Here is what Microsoft says on the subject:
Always remember, no legitimate tech support company would ever call you and any website that claims you have a virus and asks you to call a number is *****% a scam. Your computer does not report to Microsoft or any other company so if any tech support person calls you can trust it is a scam and just hang up.
What you need to do now is call your bank immediately and tell them what happened and cancel the charges. I am sure your bank will be familiar with this scam so you should be able to get your money back.
If you need further help please do not hesitate to reply back and let me know.