If a nation's real GDP is growing by 5 percent per year, its real GDP will double in approximately

Question

BlackTom AI · Accepted Answer

To determine how long it takes for real GDP to double when it grows at 5 percent per year, we can use the doubling time rule.

- Option A: 72.0 years. This would correspond to a doubling time using a rule of 72, which estimates doubling time as 72 divided by the growth rate in percent. 72/5 = 14.4, not 72, so this is incorrect for a 5% growth rate.

- Option B: 7.2 years. This would imply a much higher growth rate (roughly 72/10 ≈ 7.2%), so with a 5% growth rate, 7.2 years is too short. The math of exponential growth does not support such a rapid doubling at only 5% annual growth.

- Option C: 14.4 years. This aligns with the common rule of 72, which estimates doubling time as 72 divided by the growth rate in percent. With a 5% growth rate, 72/5 = 14.4 years, making this the reasonable approximation. Additionally, a more exact calculation using continuous compounding would yield a very close value (roughly 14.2 years), reinforcing that about 14.4 years is correct for practical purposes.

- Option D: 28.8 years. This would correspond to a doubling time at a growth rate around 2.5% (since 72/2.5 ≈ 28.8). Since the given growth rate is 5%, this option underestimates the speed of growth and is not consistent with the stated rate.

Overall, the 5% annual growth rate implies a doubling time in the mid-teens, with 14.4 years being the appropriate approximate value according to the rule of 72. The other options reflect misapplications of the rule or misinterpretation of the growth rate.

If a nation's real GDP is growing by 5 percent per year, its real GDP will double in approximately

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