Question

2. Switzerland has a per capita income of $50,000, Russia has a per capita income of $20,000, China has a per capita income of $8,000 and Liberia has a per capita income of $500. (4 points)

a. If the growth rate is 1.5% in Switzerland, 3.5% in Russia, 9% in China and 20% in Liberia, in which country is there the largest absolute increase in per capita income (absolute = in nominal value / in $)? (1 point)

Switzerland                   Russia             China              Liberia

b. Assuming a growth rate of 9%, how many years will it take for China to have a per capita income of at least $50,000? The formula is: per capita income at time t = per capita at time 0 x (1+n)^t, with n being the growth rate (9% = 9/100 = 0.09) (1 point)

10        14        18        22        26

c. Assuming a growth rate of 9%, how many years will it take for Liberia to have a per capita income of at least $50,000? (1 point)

26        38        45        54        60

d. Assuming a growth rate of 20%, how many years will it take for Liberia to have a per capita income of at least $50,000? (1 point)

26        38        45        54        60

Answer 1

Question b

Here the formula is: per capita income at time t = per capita at time 0 * (1+n) ^t

Where, n is growth rate= 9%

per capita income at time t= $50000 (final per capita income)

per capita at time 0= $8000 (initial per capita income)

we need to find t (time period)

$50000= $8000 (1+0.09)^t

$50000/$8000= (1.09)^t

So the correct option is 22

After 22 years with a growth rate of 9%, the per capita income of china will be $53268.80347, which is greater than $50000

Question c

Here the formula is: per capita income at time t = per capita at time 0 * (1+n) ^t

Where, n is growth rate= 9%

per capita income at time t= $50000 (final per capita income)

per capita at time 0= $500 (initial per capita income)

we need to find t (time period)

$50000= $500 (1+0.09)^t

$50000/$500= (1.09)^t

So, the correct option is 54

After 54 years with a growth rate of 9%, the per capita income of Liberia will be $52480.85395, which is greater than $50000

Question d

Here the formula is: per capita income at time t = per capita at time 0 * (1+n) ^t

Where, n is growth rate= 20%

per capita income at time t= $50000 (final per capita income)

per capita at time 0= $500 (initial per capita income)

we need to find t (time period)

$50000= $500 (1+0.2)^t

$50000/$500= (1.2)^t

So, the correct option is 26

After 26 years with a growth rate of 20%, the per capita income of Liberia will be $57237.72999, which is greater than $50000