Albert is paid $1 on day 1, $2 on day 2, $\ldots$, $365 on day 365.

This is the sum of the first $365$ positive integers. Use the formula:

$S = \frac{n(n + 1)}{2}$

$S = \frac{365 \times 366}{2} = \frac{133,590}{2} = 66,795$

The total amount is $66,795.