Correct. But if the debt grows faster than GDP, the debt will eventually become unsustainable.
See graph of recent times.
https://en.wikipedia.org/wiki/National_ ... States.png
You can multiply the current debt with the current interest rates and compare that to the budget to see what the effect is. Hiking a a low interest rate of 2% to 2.5% is a 0.5% increase in interest rate, but it's a 25% increase in the monthly debt payments! How much of a hike would it take to wipe out the entire budget? This tell you where "times get interesting" ...
That's too simplified. In the US case, a majority of the national debt (or close to to) is the savings of China and Japan (private and government) and so currency and trade are also involved. On a similar note, you can't have a surplus on the capital account unless you have a trade deficit.
For the man on the street, the public debt thus influences what things cost at Walmart due to the way these financial "arrangements" have been made.
Also, the private sector can put their savings in corporate bonds and if so, the public sector doesn't have to run a deficit. This may come down to how the author has defined his terms. I would highly recommend adopting a "practical" mindset here and see everything in finance as transaction and/or agreements between two entities. (Maybe I'm being Austrian here ). Those equations in your book are just formalizations of that. They might easily MISS certain aspects of what's actually going on in the real world (like other kinds of transactions).