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The Debt to GDP ratio is a very popular statics to show the level of indebtedness of a government, so much that is even used in the Euro convergence criteria. However its use seems misleading to me, since it does not account for interest rate or maturity.
I am correct that it is not a good statistics for this purpose?
If yes, why is so popular?
Wouldn't an actualized value (by a rate common to the countries be compared) of future payments be a better statistic?

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It is good statistics for the level of debt country has.

What you describe is not level of debt. A country does not have higher level of debt just because debt has shorter maturity. Moreover, interest rate country pays is completely inconsequential for the level of debt.

What you probably mean is not level of debt, but sustainability of debt. For the sustainability of debt maturity and interest rate payments would actually matter. However, debt-to-GDP is not measure of debt sustainability so there is no reason to take these into account for the variable.

I am correct that it is not a good statistics for this purpose?

No debt-to-GDP is accurate measure of debt level country has given the size of its economy. It is not a measure of debt sustainability, so one can't claim that having high debt-to-GDP, necessarily, is not sustainable for a country. However, if you just want to measure level of debt it is quite good measure.

Wouldn't an actualized value (by a rate common to the countries be compared) of future payments be a better statistic?

Not if your intention is to measure actual debt level of a country. This would measure the discounted present value of the debt of the country, which might be useful for various purposes, but it is not a measure of debt level. Also, it would make sense to use the same rate for every country since discount rate will be almost certainly heterogenous for different countries.

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