In which sentence is the underlined verb in the future perfect progressive tense?

at the age of five, she will visit new york city.

she will have been visiting new york city for a week when she turns five years old.

by the age of five, she will have visited new york city.

she will be visiting new york city when she turns five years old.

She will have been visiting New York City for a week when she turns five years old. (the second sentence)

Explanation:

The future perfect progressive is a verb tense that describes actions that will continue up until a point in the future. It consists of will + have + been + the verb's present participle (verb root + -ing).

Other options:

At the age of five, she will visit New York City. (future simple)

By the age of five, she will have visited New York City.  (future perfect)

She will be visiting New York City when she turns five years old. (future  progressive)    

better now, by post malone

the type of supporting detail is fact!