Question

Assume real per capita GDP in West Springfield is $10,000 while in East Vice City it is $2,500. The annual growth rate in West Springfield is 2.33%, while in East Vice City it is 7%. How many years will it take for East Vice City to catch up to the real per capita GDP of West Springfield?

Answer 1

31 year will be taken

Step-by-step explanation:

given data

real per capita GDP P1 = $10,000

East Vice City P2 = $2,500

annual growth rate r1 = 2.33%

East Vice City r2 = 7%

solution

we get here no of time period in year that is express here as

`P1 * (1+r1)^t = P2 * (1+r2)^t` ........................1

put here value and we will get

10000 ×
`(1+0.0233)^t` = 2500 ×
`(1+0.07)^t`

take ln both side we get

ln (
`(10000)/(2500)` ) = t × ln ( \frac{1.07}{1.0233} )

1.386294 = t × 0.04462

t = 31.068

time = 31 year