confused re ppi and large print resolution

I have a file I would like to enlarge to a 16x20 color print and am a little confused if the finished print will lose a lot of resolution.

Photo Shop Elements measurement grid shows a measured 16x20 screen image that is displayed at 100% on the screen which looks looks sharp.

Does that screen image approximate the quality of a 16x20 print made from the photo file?

The jpg file shows measures 1589 x 1181. If I extrapolate the conventional wisdom formula -

1589x1181 and divide that by 16x20 (320) i arrive at 5864 and if i get the square root of this I get only 76 pixels per inch, which is about half of the minimum 150 ppi which I have seen on these forums.

Is my reasoning correct or am I missing something?? Thanks for your help