When was the electronics correspondence course school National Radio Institute established and when did they go out of business?

The National Radio Institute (NRI) was established in 1914. While they didn't completely "go out of business" in a single moment, NRI ceased operations as an independent entity in the late 1990s/early 2000s. It was acquired and its programs were eventually absorbed into other educational companies. There's no single definitive "out of business" date, but its independent existence effectively ended around that time.