Question

What annual growth rate is needed for a country to double its output in each of the following cases? Instructions: Round your answer to one decimal place if necessary. In 7 years: % In 35 years: % In 70 years: % In 140 years: %

Answer 1

Answer:

7 years = 10.4089%, 35 years = 2%, 70 years = 0.9951%, 140 years = 0.4963%.

Explanation:

The formula for obtaining the annual growth rate in each case is

$2^{\frac{1}{years} } -1$

This is because the root of the calculation is:

PBI1 * (1+rate)^years = PBI2

where PBI2 = PBI1*2

So, clearing the PBIs:

1 * (1+rate)^years = 2

THe, for each case:

1. With 7 years = $2^{\frac{1}{7} } -1$ = 10.4089%
2. With 35 years = $2^{\frac{1}{35} } -1$ = 2%
3. With 70 years = $2^{\frac{1}{70} } -1$ = 0.9951%
4. With 140 years = $2^{\frac{1}{140} } -1$ = 0.4963%