I am completely new to economics and I have troubles understanding how the government debt of countries is computed. Imagine government of country A issue some 10 years bond of the value of 100 dollars with fixed interest rate of 5%, and government of country B issue some 10 years bond at 10 year of the value of 100 dollars with fixed interest rate of 7%. Is the government debt of the two country going to increase of 100$ each or the difference between the two interest rates is taken into account?
As originally written, parts of the question are unclear. We do not normally calculate the government debt of two countries together, they are calculated independently. Adding up debts across countries can be done, but the debts are quite oftenly in different currencies, so that would need to be taken into account.
The standard for government debt calculations is to add up the face value of all debt emitted. Yes, this does not take into account the differing interest rates, but one can usually find out the average interest rate. So in your example, both countries have debts of \$100.
(As an example, the U.S. Treasury has a webpage on “The Debt to the Penny”, with the total face value of debt; Link to FAQ. Per issue data is found in the reports available here: link to Monthly Statement of the public debt.)
One could look at the market value of government debt, but these data are not usually provided by national statistics offices. Financial data providers (bond indices) have this, but the data often misses out short-term debt, and non-marketable debt.