Question

Consider Country (Z) with a GDP level of 210,000 and a growth rate of 5% in 2019 (i.e. calculated at the end of year 2019). The experts predict that the growth of the economy of Country (Z) wills gradually slowdown in the coming years. More precisely, they foresee the following growth rates for the future: 2019 – 2022 (5%), 2022 – 2025 (3%). Hint: The list above should be read as saying that, for instance, `the growth rate from the end of 2019 until the end of 2022 will be 5%, then from the end of 2022 until the end of 2025 it will be 3%’ and so on. Requirement a) Assuming that the predictions of the experts listed above are accurate, when in the future will Country Z’s GDP double compared to the GDP level of 2019? [10 marks] b) What would Country Z’s GDP growth rate be from 2025 and so on at 1%? Explain your reasoning carefully. [5 marks] c) Consider now the more optimistic scenario in which the economy does not slow down and the current growth rate of 5% remains constant in the coming years. How long will it take for the GDP level to double in this scenario? Express your answer in two forms: i) In number of years [5 marks] ii) As a fraction of your answer in part a. [5 marks]

Answer 1

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