# Public Debt Analysis A has: -Outstanding public debt:** $2 \text{ trillion}$ - **Average interest rate:** $6\%$ per year - **GDP:** $5 \text{ trillion}$ Let's solve each part step by step. --- ## (a) Calculate Annual Interest Payments **Formula:** \[ \text{Annual Interest Payment} = \text{Public Debt} \times \text{Interest Rate} \] **Calculation:** \[ \text{Annual Interest Payment} = \$2\, \text{trillion} \times 6\% = \$2\, \text{trillion} \times .06 = \$.12\, \text{trillion} \] \[ \$.12\, \text{trillion} = \$120\, \text{billion} \] **Final Answer:** - **Annual interest payments:** **$120$ billion** --- ## (b) Interest Burden as a Percentage of GDP **Formula:** \[ \text{Interest Burden (\% of GDP)} = \frac{\text{Interest Payments}}{\text{GDP}} \times 100\% \] **Calculation:** \[ \text{Interest Burden} = \frac{\$.12\, \text{trillion}}{\$5\, \text{trillion}} \times 100\% = \frac{.12}{5} \times 100\% = 2.4\% \] **Final Answer:** - **Interest burden as a percentage of GDP:** **2.4%** --- ## (c) Analyze Sustainability Numerically **Key Points for Sustainability:** - Debt is considered **sustainable** if the government can pay interest without large deficits or needing to borrow more just to pay interest. - Compare **interest burden** to: - Typical government revenue (not given here; often 15–25% of GDP) - Economic growth rate (not given here) - Historical norms (interest payments above ~5% of GDP often cause concern) **Numerical Analysis:** - **Interest burden** is **2.4% of GDP**, which is **moderate** by historical standards. - If economic growth ($g$) exceeds the interest rate ($r$), the debt/GDP ratio can stabilize or fall, even with small primary deficits. **Rule of Thumb:** If the **interest burden is much less than 5% of GDP**, and debt is not growing rapidly, sustainability risks are low. **Numerical Conclusion:** - At **2.4% of GDP**, the interest burden is **manageable**. - Unless the primary deficit is large or interest rates rise further, the debt is **likely sustainable** in the near term. --- ## **Summary Table** | Item | Value | |------------------------------------|----------------------| | Annual interest payments | $120$ billion | | Interest burden (% of GDP) | $2.4\%$ | | Sustainability (numerical analysis)| Moderate/Manageable | --- **Final Answers** (a) **$120$ billion annual interest payments** (b) **2.4% of GDP interest burden** (c) **Numerically, the debt appears sustainable at current levels, given the moderate interest burden.**

# Public Debt Analysis Given data: - **Outstanding public debt:** $2 trillion - **Average interest rate:** 6% per year - **GDP:** $5 trillion Let's solve each part step by step. --- ## (a) Calculate Annual Interest Payments **Formula:** \[ \text{Annual Interest Payment} = \text{Public Debt} \times \text{Interest Rate} \] **Calculation:** \[ \text{Annual Interest Payment} = 2 \, \text{trillion} \times 0.06 = 0.12 \, \text{trillion} \] \[ 0.12 \, \text{trillion} = 120 \, \text{billion} \] **Final Answer:** - **Annual interest payments:** **$120 billion** --- ## (b) Interest Burden as a Percentage of GDP **Formula:** \[ \text{Interest Burden (\% of GDP)} = \frac{\text{Interest Payments}}{\text{GDP}} \times 100\% \] **Calculation:** \[ \text{Interest Burden} = \frac{0.12 \, \text{trillion}}{5 \, \text{trillion}} \times 100\% = \frac{0.12}{5} \times 100\% = 2.4\% \] **Final Answer:** - **Interest burden as a percentage of GDP:** **2.4%** --- ## (c) Analyze Sustainability Numerically **Key Points for Sustainability:** - Debt is sustainable if interest payments can be managed without excessive borrowing. - Compare interest burden to: - Typical government revenue (often 15–25% of GDP) - Economic growth rate (not given) - Historical norms (concerns arise with interest payments above ~5% of GDP) **Numerical Analysis:** - **Interest burden** is **2.4% of GDP**, which is moderate. - If economic growth ($g$) exceeds the interest rate ($r$), the debt-to-GDP ratio can stabilize or decrease, even with small primary deficits. **Rule of Thumb:** If the **interest burden is significantly less than 5% of GDP**, and the debt is not growing rapidly, sustainability risks are low. **Conclusion:** - With an **interest burden of 2.4% of GDP**, the situation appears manageable. - Unless the primary deficit increases or interest rates rise, the debt is **likely sustainable** in the near term. --- ## **Summary Table** | Item | Value | |------------------------------------|----------------------| | Annual interest payments | $120 billion | | Interest burden (% of GDP) | 2.4% | | Sustainability (numerical analysis)| Moderate/Manageable | --- **Final Answers** (a) **$120 billion annual interest payments** (b) **2.4% of GDP interest burden** (c) **Numerically, the debt appears sustainable at current levels, given the moderate interest burden.**