latest vs. late


This is a TOEIC question and I want to ask a question:

“These special rates are applied to the cars that are rented between April 01 and April 10.”

And the question was “What is the latest date that the special rates apply?” The answer is April 10.

My question is, how about “last” instead of “latest”? (My last cellphone. / My latest cellphone. - they are different, right?)

In context, I think “last” sounds better. What do you think?

Thanks in advance,

‘Last’ is possible, but ‘latest’ is not incorrect there and indicates the end of the special rate period.