Learn Finnish: Saavumme perille viimeistään maanantaina. - We will arrive at the destination on Monday at the latest.

Both express a deadline, but they work differently grammatically. Viimeistään is an adverb meaning 'at the latest'. Because it is not a postposition, the day of the week stays in its normal essive case: maanantaina (on Monday). If you wanted to use mennessä, you would need the illative case: maanantaihin mennessä (by Monday).

Why is 'perille' used here for 'at the destination'?

Perille is the standard adverb used with arriving to mean 'to the destination'. It literally comes from the word perä (the end or rear) in the allative case (-lle, onto). The phrase saapua perille is the most natural way to say you made it to where you were going.

In English we arrive 'at' a destination. Why does 'perille' use the directional 'onto' (-lle) case?

Finnish treats arriving as a movement toward a goal, rather than being statically present at it. Because of this, the verb saapua always requires an entering or directional case (illative -hVn or allative -lle). You arrive 'into' or 'onto' your destination in Finnish!

What is the base word for 'viimeistään'?

It is based on the adjective viimeinen (last). Viimeistään is a frozen superlative form that translates perfectly to the English phrase 'at the latest'.