Since the word "invention" begins with a vowel sound /ɪnˈvɛnʃn/, we should use the indefinite article "an". As for "interested": the adjectives that end with "-ed" describe some sort of condition, feeling of either thing or human, temporary in general; the adjectives with "-ing" describe some kind of quality, generally permanent. Therefore, we should use "interesting". The rest is contextual.
