Suppose the real GDP growth rate in Germany consistently averages 3.5% per year. Approximately how many years will it take for real GDP in Germany to double?

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BlackTom AI · Accepted Answer

The question asks how long it takes for real GDP to double when the growth rate is a steady 3.5% per year. This is a classic doubling-time problem often approached with the Rule of 70, which estimates doubling time as 70 divided by the growth rate in percent.

Option a. 10: If you attempted to double in 10 years, that would require a growth path much higher than 3.5% on average. Using 3.5% per year, the growth compounds to about (1.035)^10 ≈ 1.41, i.e., a 41% increase, far short of doubling. So this is too short a horizon.

Option b. 30: Doubling in 30 years would imply an average growth rate closer to 70/30 ≈ 2.33%. Since the actual rate is 3.5%, this horizon would yield more than a 2x increase, making 30 years too long relative to the given rate. The time required is shorter than 30 years.

Option c. 25: A 25-year doubling would correspond to a required rate around 70/25 = 2.8% if we used the Rule of 70. Our actual rate of 3.5% is higher, which means the doubling would occur sooner than 25 years, so this option underestimates the speed of growth.

Option d. 20: Using the Rule of 70, 70/3.5 equals exactly 20 years. This alignment shows that a steady 3.5% growth rate roughly doubles real GDP in about 20 years, given the compounding effect over time. This is the horizon implied by the stated growth rate.

Option e. 15: A 15-year doubling would require a much larger average growth rate (roughly 70/15 ≈ 4.67%). Since the actual growth is 3.5%, achieving doubling in only 15 years is implausible under the stated conditions, making this option too optimistic.

In summary, each incorrect choice either underestimates or overestimates the needed time based on how compounding at 3.5% accumulates GDP, while the 20-year estimate directly mirrors the Rule of 70 calculation for the given growth rate.

Suppose the real GDP growth rate in Germany consistently averages 3.5% per year. Approximately how many years will it take for real GDP in Germany to double?

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Suppose the real GDP growth rate in Germany consistently averages 3.5% per year. Approximately how many years will it take for real GDP in Germany to double?

Suppose the real GDP growth rate in Germany consistently averages 3.5% per year. Approximately how many years will it take for real GDP in Germany to double?

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