Question

If at the beginning of the year the public debt is $20 trillion. This year government spending is $2 trillion and transfers are $1 trillion, and tax revenues are $4 trillion. Suppose that there is an annual interest rate of 8% of debt added on at the end of the year. If GDP is $150 trillion, calculate the debt to GDP ratio at the end of the year. Instructions: If the answer is not a whole number you should leave one number after the decimal.

Answer 1

The debt to GDP ratio at the end of the year is approximately 0.156 or 15.6%. This ratio is obtained by dividing the total debt, including interest, which amounts to $21 trillion (initial debt + interest), by the GDP of $150 trillion.

Step-by-step explanation:

The debt to GDP ratio is a crucial economic indicator reflecting a country's ability to manage its debt relative to its economic output. To calculate this ratio, we start with the initial debt of $20 trillion and add the interest accrued during the year. The interest is calculated as 8% of the initial debt, which equals $1.6 trillion (20 trillion × 0.08). Therefore, the total debt at the end of the year is $21 trillion (20 trillion + 1.6 trillion).

Next, we divide the total debt by the GDP to find the debt to GDP ratio. In this case, it is $21 trillion / $150 trillion = 0.14 or 14%. This ratio signifies that the country's debt is 14% of its GDP. It provides insight into the country's fiscal health, indicating whether it can comfortably manage its debt obligations.

The debt to GDP ratio is a vital metric for policymakers and economists. A lower ratio generally suggests a healthier economy, indicating that the country is not overly burdened by debt. Conversely, a higher ratio may raise concerns about the sustainability of the debt level. In this scenario, with a debt to GDP ratio of 15.6%, the country appears to have a manageable level of debt relative to its economic output.