At the beginning of year one, there is no government debt outstanding. The government runs a \(\$ 100\) billion deficit in year one. Interest at a nominal rate of \(10 \%\) must be paid starting in year two. Assume nominal GDP in year one is \(\$ 2\) trillion, and the nominal growth rate of GDP is \(4 \%\). Assume the government balances its primary budget in the future and the interest rate and growth rate do not change.

a. What will be the government deficit in years two, three, four, and five?

b. What will be the value of government bonds outstanding at the end of the fifth year?

c. What will be the debt-GDP ratio at the end of year five?