What year was a browning BSS 12 gauge serial 7327A72 manufactured?

The (7) digit serial number of a Browning BSS breaks down like this:

The first (4) digits represent the number of the gun in the production run. yours was the 7,327 gun made that year. The next Digit "A" represents 12 Gauge (B for 20 Gauge). The final (2) digits represent the year of manufacture. In your case 1972. Hope this helps.