Assume a country, Poyais, has all its debt in foreign currency (dollars) and the local currency is called the peso.

1. Write down the debt to GDP ratio in peso terms (Hint: this should involve three variables)
2. Knowing that %(ab)=%(a)+%(b) and %(c/d)=%(c)-%(d) , rewrite the change in debt to GDP ratio in percent change terms of the three components.
3. If the peso depreciates by 10% and this increases (nominal) GDP in Poyais by 5%, what happens to the debt to GDP ratio in peso terms?
4. Write down the interest payments on Poyais debt in peso terms as a ratio to GDP (Hint: this involves adding one variable to your answer to the above).
5. Knowing that %(ab)=%(a)+%(b) and %(c/d)=%(c)-%(d) , rewrite the change in interest payments to GDP ratio in percent change terms.
6. Assume that central bank of Poyais (headquartered in Saint Joseph) hikes interest rates, which cause the interest rate on the Poyais debt to rise by 4%, and which causes GDP in Poyais to fall by 7%. By how much would the peso to dollar exchange rate have to appreciate for interest payments as a share of GDP to remain the same as before interest rates were hiked?