GDP & Debt

Consider a hypothetical country named Dreamland.

It has a GDP of $10,000,000.

It has a total debt of $8,000,000. (80% of GDP)

The bond market will buy Dreamland's bonds at a 5% interest rate.

Total interest charges in Dreamland are therefore $400,000 annually.

Dreamland is a developed country that grows at 3% annually ($300,000 in this example).

Therefore we see that the debt will increase at $100,000 per year as the country can not grow faster than its interest charges.  The sovereign debt becomes a ponzi system as there is no hope of repaying even just the interest on the debt, never mind the principal.

How long will the bond market continue to finance Dreamland?

Not long.

Consider the following countries with their respective Debt to GDP ratios:
Source of this information is the CIA World Factbook - GDP as of 2009.

We see that Japan, US and Greece are already beyond the 80% point of no return.  Many developed countries are about to cross the threshold including Germany, Portugal and Canada.  The UK is a special case.  Although it's debt is not as high as other developed countries, it has massive private debt that effectively puts it beyond the point of no return threshold.

Will governments be able to repay these direct debts?

When hippos fly.