Back of the envelope math:

Let’s assume the initial debt is D and the initial GDP is G. The initial debt-to-GDP ratio is D/G.

Let's say the new debt is 1.2D (20% higher) and the new debt-to-GDP ratio is 0.9(D/G) (10% lower).

We can set up an equation using the new debt and the new debt-to-GDP ratio:

1.2D / New GDP = 0.9(D/G)

We want to find the New GDP, so we'll rearrange the equation:

New GDP = 1.2D / (0.9(D/G))

Simplifying:

New GDP = 1.2D / (0.9D/G)

New GDP = 1.2 / 0.9 * G

New GDP = 1.333G

This means the new GDP is approximately 33.3% higher than the initial GDP.

To find out how much real GDP was created with the new debt, we subtract the initial GDP from the new GDP:

Increase in GDP = New GDP - Initial GDP

= 1.333G - G

= 0.333G

So, approximately 33.3% of the initial GDP was created with the new debt.

In terms of actual value, if we assume D = $100 trillion and G = $100 trillion initially (debt-to-GDP ratio of 100%), then:

Initial Debt: $100 trillion

Initial GDP: $100 trillion

New Debt: $120 trillion (20% higher)

New Debt-to-GDP Ratio: 90% (10% lower)

Using our previous calculation:

New GDP ≈ $133.33 trillion

Increase in real gdp ≈ $33.33 trillion