Answer:
Country (Z) GDP Growth:
a) The GDP will double in:
2019 - 2022 = 3 years
2022 - 2025 = 3 years
2025 to 20 years as determined below
Total = 26 years
The GDP will double in 26 years.
b) The growth rate from 2025 and so on at 1% will approach 27.62% based on the 2019 GDP. The approach used is to determine the difference between the after 2025 GDP and the 2019 GDP. This difference (growth in absolute terms) is divided by the 2019 GDP, and then multiplied by 100 to obtain the rate.
c) If the growth rate of 5% is sustained, it will take the GDP 15 years to double:
420,000 = G₀(1 + g)ⁿ
420,000 = 210,000 (1 + 5%)ⁿ
Solving for n with an online calculator,
n = 15 years
Check:
210,000 x 2.079
= 436,590
= 437,000 approx.
As a number of years = 15 years
As a fraction of part a answer = 15/26 = 57.69%
Explanation:
a) 2019 Country Z's GDP = 210,000
2019 - 2022 Growth rate = 5%
Future growth rates:
2022- 2025 = 3%
2025 - so on = 1%
Let Country (Z's) GDP in 2019 = G₀ which is equal to 210,000
n = number of years from 2019 to 2022, 2022 to 2025, and so on.
g = growth rate = 5% for the period 2019 to 2022
Gⁿ = GDP in n years at given rates
Gⁿ = G₀(1 + g)ⁿ
(1 + g)ⁿ = increase in GDP as a result of the growth rate and number of years
b) With GDP growth of 5% from 2019 to 2022, the GDP will be
= 210,000 (1 + 5%)³
= 210,000 x 1.158
= 243,000 approx.
c) From 2022 to 2025 at 3%, the GDP will be
= 243,000 (1 + 3%)³
= 243,000 x 1.093
= 265,600
For GDP to double the 2019 GDP with 3% growth = 420,000 (210,000 x 2) or more
GDP = Gⁿ = G₀(1 + g)ⁿ
420,000 = 243,000 (1 + 3%)ⁿ
solving for n with an online calculator,
n = 20
Check:
= 243,000 (1 + 3%)∧20
= 243,000 x 1.817
= 441,531
= 442,000
