Question

Suppose a country is producing $20 million of real gdp. If the economy grows at 10 percent per year, approximately how many years will to take for real gdp to grow to $80 million?.

Answer 1

It will take approximately 14 years for the real GDP of a country to grow from $20 million to $80 million at an annual growth rate of 10 percent.

Step-by-step explanation:

To determine how long it will take for a country's real GDP to grow from $20 million to $80 million at a growth rate of 10 percent per year, we can use the formula for exponential growth:

`\text{Future value} = \text{Present value} * (1 + \text{growth rate})^(years)`

In this case, we want to solve for the time (years) it will take for the real GDP to quadruple. Now, substituting the given values:

$80 million = $20 million ×
`(1 + 0.10)^(years)`

`4 = (1.10)^{years`

Using logarithms, we can solve for the number of years:

years = log(4) / log(1.10)

years ≈ 14.21

Therefore, it takes approximately 14 years for the real GDP to grow to $80 million.