Question

The fictitious country "Alpha" has a real GDP per person of $10,000.

Instructions: Enter your responses rounded to the nearest penny (two decimal places).


a. If Alpha has a 1% growth rate in real GDP per person, then after 10 years Alpha's real GDP per person is $

b. If Alpha has a 2% growth rate in real GDP per person, then after 10 years Alpha's real GDP per person is $

c. After 10 years, the difference in Alpha's real GDP per person based on the two growth rates is $

Answer 1

Using the compound growth formula, Alpha's real GDP per person after 10 years is $11,046.22 for a 1% growth rate and $12,189.94 for a 2% growth rate. The difference between the two after 10 years is $1,143.72.

Step-by-step explanation:

Calculating the Real GDP per Person Growth

To calculate the future value of real GDP per person, we use the formula for compound growth:

GDP_{future} = GDP_{current} \times
`(1 + growth rate)^(years)`

a. With a 1% growth rate:

GDP_{future} = $10,000 \times
`(1 + 0.01)^(10)` = $10,000 \times
`1.01^(10)`= $10,000 \times 1.104622125 = $11,046.22

b. With a 2% growth rate:

GDP_{future} = $10,000 \times
`(1 + 0.02)^(10)` = $10,000 \times
`1.02^(10)` = $10,000 \times 1.21899428 = $12,189.94

c. The difference in GDP per person between the two growth rates:

Difference = $12,189.94 - $11,046.22 = $1,143.72

Answer 2

a. After 10 years, Alpha's real GDP per person with a 1% growth rate is $11,046.41

Calculation: $10,000*(1.01)^10 = $11,046.41

b. After 10 years, Alpha's real GDP per person with a 2% growth rate is $12,189.94

Calculation: $10,000*(1.02)^10 = $12,189.94

c. After 10 years, the difference in Alpha's real GDP per person based on the two growth rates is $1,143.53

Calculation: $12,189.94 - $11,046.41 = $1,143.53