Assume that an economy grows at compounding rates.Then, over a period of 40 years, an economy that grows at 6.5% each year will have an output level approximately ____ times larger than an economy that grows at 2.5%.

Question

Quizplus · Accepted Answer

To calculate the increase in output level after 40 years for an economy that grows at 6.5% each year, we can use the compound interest formula:
Output level after 40 years = Initial output level x (1 + growth rate)^40

Similarly, for an economy that grows at 2.5% each year, we have:
Output level after 40 years = Initial output level x (1 + growth rate)^40

Dividing the output level of the first economy by the output level of the second economy, we get:
Output level after 40 years (6.5% growth rate) 
------------------------------------------------- = (1.065^40) / (1.025^40)
Output level after 40 years (2.5% growth rate)

Calculating this using a calculator yields approximately 5. Therefore, an economy that grows at 6.5% each year will have an output level approximately five times larger than an economy that grows at 2.5%. Hence the correct answer is C) five.

Assume That an Economy Grows at Compounding Rates