Sample Questions on Growth Rate

Question 1: The population of a city was 500,000 in 2010 and increased to 600,000 in 2020. Calculate the simple growth rate (SGR) of the city’s population over the decade.

Solution:

To calculate the SGR:

SGR = ((Final Value – Initial Value) / Initial Value) × 100%

SGR = ((600,000 – 500,000) / 500,000) × 100%

= (100,000 / 500,000) × 100%

= 0.2 × 100% = 20%

Therefore, the simple growth rate of the city’s population over the decade is 20%.

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Question 2: The revenue of a company was $2,000,000 in 2015 and increased to $2,800,000 in 2020. Calculate the compound annual growth rate (CAGR) of the company’s revenue over the five-year period.

Solution:

To calculate the CAGR:

CAGR = ((Final Value / Initial Value)^(1/n)) – 1

= ((2,800,000 / 2,000,000)^(1/5)) – 1

≈ (1.4^(0.2)) – 1

≈ 1.1487 – 1 ≈ 0.1487 or 14.87%

Therefore, the compound annual growth rate of the company’s revenue over the five-year period is approximately 14.87%.

Question 3: The GDP of a country was $1.5 trillion in 2010 and increased to $2.5 trillion in 2020. Calculate the simple growth rate (SGR) and compound annual growth rate (CAGR) of the country’s GDP over the decade.

Solution:

SGR = ((2,500,000,000,000 – 1,500,000,000,000) / 1,500,000,000,000) × 100%

= (1,000,000,000,000 / 1,500,000,000,000) × 100%

= 0.6667 × 100%

= 66.67%

CAGR = ((2,500,000,000,000 / 1,500,000,000,000)^(1/10)) – 1

≈ (1.6667^(0.1)) – 1

≈ 1.1072 – 1 ≈ 0.1072 or 10.72%

Therefore, the simple growth rate of the country’s GDP over the decade is 66.67%, and the compound annual growth rate is approximately 10.72%.

Question 4: A company’s stock price was $50 per share in 2018 and increased to $70 per share in 2021. Calculate the simple growth rate (SGR) of the company’s stock price over the three-year period.

Solution:

SGR = ((70 – 50) / 50) × 100%

= (20 / 50) × 100%

= 0.4 × 100% = 40%

Therefore, the simple growth rate of the company’s stock price over the three-year period is 40%.

Question 5: The number of subscribers to a streaming service was 50 million in 2017 and increased to 100 million in 2021. Calculate the compound annual growth rate (CAGR) of the streaming service’s subscriber base over the four-year period.

Solution:

CAGR = ((100,000,000 / 50,000,000)^(1/4)) – 1

= (2^(0.25)) – 1

= 1.1892 – 1 = 0.1892 or 18.92%

Therefore, the compound annual growth rate of the streaming service’s subscriber base over the four-year period is approximately 18.92%.

Growth rate is essential for analyzing changes over time in various fields, from finance and economics to population dynamics and scientific research. Whether you’re assessing the growth of an investment, the expansion of a business, or the increase in population, knowing how to calculate the growth rate accurately is invaluable.

In this article, we’ll explore different methods of calculating growth rates and provide examples to help you master this fundamental concept.