In this year,Country A has a real GDP per person that is 4 times greater than that of Country B.Country B's growth rate of real GDP per person is 3.5 percent per year.How many years will it take for Country B's real GDP per person to reach the same level that Country A had in this year?

Question

Quizplus · Accepted Answer

Let's assume that in Country A, the real GDP per person is $100.
Therefore, in Country B, the real GDP per person is $25 ($100/4).
If Country B's growth rate of real GDP per person is 3.5 percent per year, then after one year, the real GDP per person in Country B will be:
$25 + ($25 x 0.035) = $25.88
To find out how many years it will take for Country B's real GDP per person to reach $100 (the same level as Country A), we need to use the formula for compound interest:
FV = PV x (1 + r)n
where:
FV = future value
PV = present value
r = annual interest rate
n = number of years
Let's plug in the numbers:
$25.88 = $25 x (1 + 0.035)n
Divide both sides by $25:
1.03552 = 1.035n
Take the natural log of both sides:
ln(1.03552) = n x ln(1.035)
n = ln(1.03552) / ln(1.035)
n ≈ 39.9 years
So it will take about 40 years for Country B's real GDP per person to reach the same level that Country A had in this year. Therefore, the best choice is C) 40 years.

In This Year,Country a Has a Real GDP Per Person