1a. before long; without undue delay b. in a short time; soon 2. at the present time; now

Here’s a word for the dueling dictionaries. Note the contrasting emphasis between the American Heritage Dictionary and Webster’s: An original meaning of presently was “at the present time; currently.”
American Heritage: “That sense is said to have disappeared from the literary language in the 17th century, but it has survived in popular usage and is widely found nowadays in literate speech and writing. Still, there is a lingering prejudice against this use.“
Webster’s: “Both senses 1 and 2 are flourishing in current English, but many commentators have objected to sense 2. Since this sense has been in continuous use since the 15th century, it is not clear why it is objectionable.”
Ooooh! Them’s fightin’ words!