Learn Turkish: Yatıracağını kendisi biriktirebildi. - He managed to save what he will invest himself.

This is a headless relative clause using the future participle -acak. The root is yatır- (to invest). We add -acak (future), but the k softens to ğ because it is followed by a vowel. Then we add the possessive suffix -ı (his), making it yatıracağı (the thing he will invest). Since there is no noun after it like "money", the participle itself acts as the noun.

Why are there two -ı suffixes at the end of yatıracağını?

The first -ı is the 3rd person possessive suffix, which is required in this type of relative clause to show who is doing the investing (literally "his future invested thing"). The second -ı is the accusative case marker. Because "what he will invest" is the direct object of the verb "save", it takes the accusative case. The -n- in the middle is a buffer letter used when adding case markers to 3rd person possessive suffixes.

Could we just use o (he) instead of kendisi?

You could use o, but kendisi adds specific emphasis. Kendi means "self" and adding the 3rd person possessive -si makes it "he himself". Using it here stresses that he managed to save the money on his own, without outside help.

How do we get "managed to" from biriktirebildi?