cf. I saved money to buy a new computer.

Does 'to buy a new computer' modify 'money' and an adjective phrase?

Or is 'to buy a new computer' an adverbial phrase?

The phrase "to buy a new computer" is an adverbial phrase telling WHY you saved.

In the given sentence, "to buy a new computer" functions as an adverbial phrase. It clarifies the purpose or intention behind saving the money. Adverbial phrases provide additional information about the verb, explaining why, how, or to what extent an action is performed.

To determine whether a phrase is adjectival or adverbial, we can consider its function and what it modifies:

1. Adjectival phrases modify a noun or pronoun, providing more details or descriptions about it.

Example: "The book on the shelf is mine." ("on the shelf" modifies the noun "book")

2. Adverbial phrases modify a verb, adjective, or other adverbs, providing information about time, place, manner, purpose, or condition.

Example: "He ran to catch the bus." ("to catch the bus" modifies the verb "ran")

In your sentence, "to buy a new computer" modifies the verb "saved." It explains the purpose or intention behind saving the money, making it an adverbial phrase.