Should be more like $25k IMO, unless he got some crazy bonuses for overseas deployment or the like.
E4 - Petty Officer - 3rd Class (Navy) Salary | Salary.com
My guess:
He was a Submarine ET. He'd be entitled to a few proficiency pay bonuses, and would promote to E4 right away during school. Shortly after that, he could easily make E5, where he'd also be entitled to live off the ship and thus collect a housing allowance. Many E4/E5's collecting BAH live with roommates and are able to save some of that allowance.
E5 over 4 makes $2550 base/month. It doesn't say where he was living, but let's assume Norfolk (largest base in the world). His housing allowance there would be $1200/month. That's $3750/month so far.
He's on sea duty, so he collects sea pay: $160/mo under 2 years, up to $350/mo once he's over 3 years sea duty (usually one tour for the enlisted guys). So let's say he stays at $160...
Now up to ~$3900/mo.
If he's a submarine ET, that's another $155/mo for sub pay... now $4150/mo. That's right at $50,000/yr for an E5 at 4 years of service, which is quite possible if not likely in that rating.
Depending on housing allowance, how much time he had at sea, how long he actually served, he could easily be making $55,000 per year as a first term sailor. If he had a nuclear specialty, he'd have other bonuses even as an E4 that could push him toward that range.
There's nothing wrong with his salary projection.