I have a new iMac 21.5 in Icant find the memory port to install new memory

The iMac 21.5 inch model does not have user upgradable RAM, you would need to take it to an Apple Authorised Service Provider.

Please read this Apple article, and pay special attention to the information in the blue box.

Install memory in an iMac – Apple Support

Whaaa??? I am flabbergasted. I bought this assuming it would be easy to upgrade the RAM but today the Apple tech told me it would be $700 or so to upgrade. I am stunned that there would not be a door to access to install more RAM.

Well you should have read the specifications before you bought it.

The 21.5 inch iMac is a totally sealed unit, there are no removable panels, you can plainly see that from the design.

In order to insert RAM the whole casing has to be removed, as it is bonded with glue it is a tricky process and thus

the large cost.

Should have ordered the extra RAM when you ordered it.

Did you buy it direct from Apple or did you buy it from another reseller, perhaps their returns policy is different.

You have 14 days to return it.

And I am way past the 14-day return window. Surely other people have had the same problem.

I am past that window, and was told today by an Apple tech that it would cost $700-800 to add RAM. I am both astonished and stunned by the design and the cost.

Me too. it's a crime. :(

One thing that can help alleviate the shortage of RAM is to boot from an external SSD...

https://eshop.macsales.com/shop/external-drives/OWC-Envoy-Pro

Thanks for pointing that out, Eau - you are absolutely right it is my fault. I hadn’t thought about it that way.