Real GDP per person in the country of Flip is $10,000, and the growth rate is 10 percent a year. Real GDP per person in the country of Flap is $20,000 and the growth rate is 5 percent a year. When will real GDP per person be greater in Flip than in Flap?

Question

Quizplus · Accepted Answer

To find out when real GDP per person in Flip will be greater than that of Flap, we need to calculate when the two countries will have the same real GDP per person. Let's call this time T.

Real GDP per person in Flip can be represented as: 
GDP per person in year 0 * (1 + growth rate)^T

Real GDP per person in Flap can be represented as: 
GDP per person in year 0 * (1 + growth rate)^T

We know that GDP per person in Flip is $10,000 and the growth rate is 10% a year. So: 
$10,000 * (1 + 0.10)^T

We also know that GDP per person in Flap is $20,000 and the growth rate is 5% a year. So: 
$20,000 * (1 + 0.05)^T

Now we set the two equations equal to each other and solve for T:

$10,000 * (1 + 0.10)^T = $20,000 * (1 + 0.05)^T

Simplifying: 
(1.10)^T = (1.05)^T * 2

Taking the natural logarithm of both sides: 
T * ln(1.10) = ln(2) + T * ln(1.05)

T * (ln(1.10) - ln(1.05)) = ln(2)

T = ln(2) / (ln(1.10) - ln(1.05)) ≈ 14.7

Therefore, it will take about 15 years for real GDP per person in Flip to be greater than that of Flap. So the answer is D) in 15 years.

Real GDP Per Person in the Country of Flip Is