Readers Question: Is it possible for a country to completely pay off its national debt?
Yes. A country with an easy source of tax (e.g. oil-rich Middle-East countries) could easily run a budget surplus and buy back any previous government bonds.
It is possible people may not want to sell bonds to the government; they might like to keep the investment which promises to pay a guaranteed interest rate. In that case, the government would have to wait until the bonds expire at the end of their 10, 20 or 30 year period.
According to CIA Factbook, the country with the lowest national debt as a % of GDP is Liberia  with 3.3% of GDP.
Is it desirable to pay off the national debt?
A problem with paying off the national debt is that the country would effectively have no bond market. People with savings wouldn’t be able to choose the secure option of buying government bonds. It might encourage domestic savers to look abroad and buy bonds in other countries – causing an outflow of money.
Running a persistent budget surplus could also depress aggregate demand. The government is effectively withdrawing money from the circular flow of money.
If you look at countries with the lowest national debt as a % of GDP – they are not particularly countries with the best living standards.
Liberia, Libya, Oman, Kuwait, Takikstan, Estonia.