You're making the mistake of considering these as independent variables and extending them to infinity assuming no one will respond to current state of the worl

You're making the mistake of considering these as independent variables and extending them to infinity assuming no one will respond to current state of the world in the future. The only way the fed will keep rates at 5% for 30 years would be if we had a gangbusters overheating economy going full tilt with near zero unemployment for the entire time. In which case the GDP graph will be up and to the right the entire time. And in that scenario GDP (and thus tax income) will be rising faster than debt and interest payments rise. Put that aside though and assume that we somehow end up in a situation where debt servicing is a huge chunk of the budget. There are tools to solve that problem. We can accept more immigrants and give more incentives for existing citizens to have kids to kickoff population growth. We can increase tax rates to payoff some of the debt. If you want to get esoteric the Treasury can mint coins and deposit them at the Fed - something the US Government does every year, creating brand new money out of nothing. Yes this would amount to some monetization of the debt but it is a possibility. All of these strategies and many more have pros and cons. Perhaps in reality we'd use a mix of many different strategies.