Question

Consider country Z with a GDP level of 210000 and a growth rate of 5% in 2019 (ie calculated at the end of year 2019). The experts predict that the growth of the economy of country Z will gradually slowdown in the coming year. More precisely, they foresee the following growth rate for the future: 2019-2022 (5%), 2022-2025 (3%).

a. Assuming that the prediction of the experts listed above are accurate, when in the future will country Z's GDP double compared to the GDP level of 2019??
b. What would country Z's GDP growth rate be from 2025 and so on at 1%. Explain your reasoning carefully​

Answer 1

a. Country Z's GDP will double in 23 years' time, given the experts prediction of 5% growth for 3 and 3% thereafter.

b. Z's GDP 's growth rate would be 39%.

This growth rate is calculated by determining Z's GDP from the end of 2025 as 292,000. So, (292,000 - 210,000)/210,000 x 100 = 39% from the 2019 base year.

Explanation:

a) 2019 Country Z's GDP = 210,000

2019 Growth rate = 5%

Future growth rate:

2019 - 2022 = 5%

2022- 2025 = 3%

2025 - so on = 1%

Let Country Z's GDP in 2019 = G₀ = 210,000

n = number of years from 2019

g = growth rate = 5%

(1 + g)ⁿ = increase in GDP as a result of the growth rate and number of years

Gⁿ = GDP in n years

Therefore, Gⁿ = G₀(1 + g)ⁿ

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%)∧20

= 243,000 x 1.817

= 441,531

d) Z's GDP from 2025 with 1% growth and so on, will become double at:

Gⁿ = 265,600(1 + 1%)∧48

= 265,600 x 1.61

= 428,000

48 + 6 = 54 years.