age vs period of time

age and period of time both are nouns.

Word	Noun	Adjective	Verb	Adverb
age	Yes	No	Yes	No
period of time	Yes	No	No	No

As nouns, period of time is a hypernym of age; that is, period of time is a word with a broader meaning than age:

Other hypernyms of age include period, time period.

age (noun)	period of time (noun)
how long something has existed	an amount of time
a time of life (usually defined in years) at which some particular qualification or power arises
a late time of life
an era of history having some distinctive feature
a prolonged period of time