Question

if a country's debt-to-gdp ratio is currently 15% and its debt is expected to grow from 2 trillion dollars to 3 trillion dollars in the next 5 years what will the country's GDP have to be in five years to maintain the current debt-to-gdp ratio

Answer 1

If the current debt is 2 trillion dollars, then the GDP must be 2/1.15=$1.7391 X 10^12. If the ratio of 15% must be maintained in 5 years time, then the GDP must grow to: 3/2 X 1.7391 X 10^12

=$2.60865 X 10^12. Because: 3 X 10^12/2.60865 X 10^12=1.15=15%

Answer 2

Hence, the new country's GDP have to be 20 trillion dollars in order to maintain the current debt to gdp-ratio.

Explanation:

if a country's debt-to-gdp ratio is currently 15%.

If the current debt(d) is 2 trillion dollars, then the initial GDP(g) must be

`(d)/(g)=15\%=0.15`

Here d=2

Hence
`g=(2)/(0.15)=13.33`

Hence, the current GDP or initial GDP is 13.33 trillion dollar.

Now after 5 years the debt is expected to be 3 trillion dollars i.e. d'=3 trillion dollars.

Let the new GDP be denoted by g'

Hence,

`(d'-d)/(g'-g)=0.15\\ \\(3-2)/(g'-13.33)=0.15\\\\(1)/(g'-13.33)=0.15\\\\(1)/(0.15)=g'-13.33\\\\g'=20`

Hence, the new country's GDP have to be 20 trillion dollars in order to maintain the current debt to gdp-ratio.