Question

Item 24 Time Remaining 31 minutes 59 seconds 00:31:59 Item 24 Item 24 Time Remaining 31 minutes 59 seconds 00:31:59 Real GDP per person in both Alpha and Omega is equal to $2,000. Over the next 100 years, real GDP per person grows at a 1.5 percent annual rate in Alpha and at a 2.5 percent annual rate in Omega. After 100 years, real GDP per person in Alpha is ______ smaller than real GDP per person in Omega.

Answer 1

After 100 years, real GDP per person in Alpha is 4 TIMES smaller than real GDP per person in Omega.

Step-by-step explanation:

Current real GDP per capita in Alpha = $2,000

in 100 years, the real GDP per capita in Alpha = $2,000 x (1 + 1.5%)¹⁰⁰ = $5,848.87

Current real GDP per capita in Omega = $2,000

in 100 years, the real GDP per capita in Omega = $2,000 x (1 + 2.5%)¹⁰⁰ = $23,627.43

Alpha's real GDP per capita is 4 times smaller than Omega's = $23,627.43 / $5,848.87 = 4.04 times

*I used the future value formula: FV = PV (1 + r)ⁿ