at a price of/ at a cost of

I would like to know which alternative should I use:
‘Now a new, modern library has been built in Alexandria, at a cost / price of 120m pounds.’
I have no idea, ‘price’ sounds fine for me.
Thank you for your time!

I would suggest ‘at a cost of’ indicates a grand total for a project or scheme whereas ‘at a price of’ would probably be used for individual items as in - They bought the cheese for the shop at a price of x£ per kilo.