Aplia QESTION 2. Growth experiences Small differences in the rate of economic gr
ID: 1190439 • Letter: A
Question
Aplia QESTION
2. Growth experiences
Small differences in the rate of economic growth can lead to large differences in living standards. Consider two countries, Fritolaysia and Khandibar. Currently, real GDP per person (average income) is $100,000 in Fritolaysia and $25,000 in Khandibar.
Use the growth formula to fill in the following table. Round your answers to the nearest dollar.
Average Income after 100 Years
(Dollars)
Suppose Fritolaysia's growth rate is expected to grow at 1.4% and remain there for the next 100 years. Which of the following growth rates in Khandibar would cause the average income in Khandibar to exceed the average income in Fritolaysia in 100 years? Check all that apply.
A. 1.4%
B. 1.6%
C. 4.0%
D. 4.2%
Aplia QESTION
2. Growth experiences
Small differences in the rate of economic growth can lead to large differences in living standards. Consider two countries, Fritolaysia and Khandibar. Currently, real GDP per person (average income) is $100,000 in Fritolaysia and $25,000 in Khandibar.
Suppose you want to project what the real GDP per person will be in each country 100 years from now. The following formula shows how to compute the average income in years, where represents the growth rate of real GDP per person (in decimal form—that is, 1.4% is entered as 0.014) and represents the number of years:
Use the growth formula to fill in the following table. Round your answers to the nearest dollar.
Growth RateAverage Income after 100 Years
(Percent)(Dollars)
Fritolaysia Khandibar 1.4 ___________ ___________ 1.6 ___________ ___________ 4 ___________ ___________ 4.2 ___________ ___________Suppose Fritolaysia's growth rate is expected to grow at 1.4% and remain there for the next 100 years. Which of the following growth rates in Khandibar would cause the average income in Khandibar to exceed the average income in Fritolaysia in 100 years? Check all that apply.
A. 1.4%
B. 1.6%
C. 4.0%
D. 4.2%
Explanation / Answer
Calculate average income in Fritolaysia after hundred years -
Case I -
Current average income - $100,000
Growth rate - 1.4% or 0.014
Time = 100 years
Average income in 100 years = Current average income * (1 + growth rate)n
= $100,000 * (1+0.014)100
= $401,600
The average income in 100 years at growth rate of 1.4% will be $401,600.
Case II -
Current average income - $100,000
Growth rate - 1.6% or 0.016
Time = 100 years
Average income in 100 years = Current average income * (1 + growth rate)n
= $100,000 * (1+0.016)100
= $489,000
The average income in 100 years at growth rate of 1.6% will be $489,000.
Case III -
Current average income - $100,000
Growth rate - 4% or .04
Time = 100 years
Average income in 100 years = Current average income * (1 + growth rate)n
= $100,000 * (1+0.04)100
= $5,050,000
The average income in 100 years at growth rate of 4% will be $5,050,000.
Case IV -
Current average income - $100,000
Growth rate - 4.2% or 0.042
Time = 100 years
Average income in 100 years = Current average income * (1 + growth rate)n
= $100,000 * (1+0.042)100
= $6,120,000
The average income in 100 years at growth rate of 4.2% will be $6,120,000.
Calculate average income in Khandibar after hundred years -
Case I -
Current average income - $25,000
Growth rate - 1.4% or 0.014
Time = 100 years
Average income in 100 years = Current average income * (1 + growth rate)n
= $25,000 * (1+0.014)100
= $100,400
The average income in 100 years at growth rate of 1.4% will be $100,400.
Case II -
Current average income - $25,000
Growth rate - 1.6% or 0.016
Time = 100 years
Average income in 100 years = Current average income * (1 + growth rate)n
= $25,000 * (1+0.016)100
= $122,250
The average income in 100 years at growth rate of 1.6% will be $122,250.
Case III -
Current average income - $25,000
Growth rate - 4% or 0.04
Time = 100 years
Average income in 100 years = Current average income * (1 + growth rate)n
= $25,000 * (1+0.04)100
= $1,262,500
The average income in 100 years at growth rate of 4% will be $1,262,500.
Case IV -
Current average income - $25,000
Growth rate - 4.2% or 0.042
Time = 100 years
Average income in 100 years = Current average income * (1 + growth rate)n
= $25,000 * (1+0.042)100
= $1,530,000
The average income in 100 years at growth rate of 4.2% will be $1,530,000.
Following is the complete table -
Table 1
Growth Rate
(Percent)
Average Income after 100 years
(Dollars)
Fritolaysia
Khandibar
1.4
401,600
100,400
1.6
489,000
122,250
4
5,050,000
1,262,500
4.2
6,120,000
1,530,000
As above table shows that if Fritolaysia's growth rate is expected to grow at 1.4% and remain there for next 100 years then Khandibar must grow at either 4% or 4.2% because in both these cases the average income in Khandibar in 100 years would exceed the average income in Fritolaysia in 100 years.
Hence, the correct answer is both option C and D.
Growth Rate
(Percent)
Average Income after 100 years
(Dollars)
Fritolaysia
Khandibar
1.4
401,600
100,400
1.6
489,000
122,250
4
5,050,000
1,262,500
4.2
6,120,000
1,530,000
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