Respuesta :
Answer:
20 years (scenario A) and 16 years (scenario B)
Explanation:
The real GDP will double in "n" number of years, with "n" estimated by interpolation using the formula below.
[tex]current GDP * (1+Growth Rate)^{n} = 2 * current GDP[/tex]
In the solutions below, we assumed current GDP to be 1, and as a result, the GDP will double to 2.
Scenario A
[tex]1 * (1+0.35)^{n} =2[/tex]
When you substitute 20 for "n" in the left hand side (LHS) of the equation, you will arrive at 1.99 which is approximately equal to 2. Any number below 20 will result in a number less than 2.
Thus, with an average annual real GDP growth rate of 3.5%, real GDP will double in about 20 years.
Scenario B
[tex]1 * (1+0.45)^{n} =2[/tex]
When you substitute 16 for "n" in the left hand side (LHS) of the equation, you will arrive at 2.02 which is approximately equal to 2. Any number below 16 will result in a number less than 2.
Thus, with an average annual real GDP growth rate of 4.5%, real GDP will double in about 16 years.
