Debt dynamics

A government has debt of 82% of GDP, pays an effective nominal rate of 7.3% and has nominal GDP growth of 10% (hypothetical). (a) With a primary deficit of 2% of GDP, compute next year's debt ratio. (b) Find the primary balance that stabilises the ratio. (c) Repeat (a) and (b) with $i=8.5\%$ and $g_n=8\%$, a stylised "hiking into a slowdown". (d) Relate your answer to Dalio's long-term debt cycle.