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Assume real per capita GDP in West Swimsuit is $10,000 while in East Quippanova it is $2,500. The annual growth rate in West Swimsuit is 2.33%, while in East Quippanova it is 7%. How many years will it take for East Quippanova to catch up to the real per capita GDP of West Swimsuit? Choose one:
A. about 10 years
B. about 30 years
C. about 40 years
D. about 120 years
E. East Quippanova will never be able to catch up with West Swimsuit

Respuesta :

Answer:

correct option is B. about 30 years

Explanation:

given data

real per capita GDP west = $10,000

annual growth rate = 2.33%

real per capita GDP east = $2,500

annual growth rate = 7%

to find out

How many years will it take for East  to catch up GDP of West

solution

we know here that future value is equal to real GDP of west after time  will be

future value = real per capita GDP west × [tex]rate^{t}[/tex]

future value = 10000 × [tex](1+0.0233)^{t}[/tex] .....1

and

future value = real per capita GDP east × [tex]rate^{t}[/tex]

future value = 2500 × [tex](1+0.07)^{t}[/tex] .....2

compare equation 1 and 2

10000 × [tex](1+0.0233)^{t}[/tex]  = 2500 × [tex](1+0.07)^{t}[/tex]

4 [tex](1.0233)^{t}[/tex]  =  [tex](1.07)^{t}[/tex]

t = about 30 years

so correct option is B. about 30 years

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