At the beginning of year one, there is no government debt outstanding. The government runs a $$100$ billion deficit in year one. Interest at a nominal rate of $10\%$ must be paid starting in year two. Assume nominal GDP in year one is $$2000$ billion 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?