Assume that per capita income is growing at different rates in the following countries: Nepal, 1.0 percent; Kenya, 1.6 percent; Singapore, 7.3 percent; Egypt, 3.4 percent. How long will it take for each country to double its income per person?

Nepal

70 years

Kenya

47 years

Singapore

10 years

Egypt

21 years

Explanation:

Suppose

Time period = X

Per capita Income = $1

Using following formula calculate time period to double the per capital Income

FV = PV ( 1 + g)^n

Nepal

g = 1%

2 x $1 = $1 ( 1 + 0.01)^n

$2 / $1 = 1.01^n

$2 = 1.01^n

Log 2 = n Log 1.01

log 2 / log 1.01 = n

n = 69.66 years = 70 years

Kenya

g = 1.6%

2 x $1 = $1 ( 1 + 0.016)^n

$2 / $1 = 1.016^n

$2 = 1.016^n

Log 2 = n Log 1.016

log 2 / log 1.016 = n

n = 43.66 years = 47 years

Singapore

g = 7.3%

2 x $1 = $1 ( 1 + 0.073)^n

$2 / $1 = 1.073^n

$2 = 1.073^n

Log 2 = n Log 1.073

log 2 / log 1.073 = n

n = 9.84 years = 10 years

Egypt

g = 3.4%

2 x $1 = $1 ( 1 + 0.034)^n

$2 / $1 = 1.034^n

$2 = 1.034^n

Log 2 = n Log 1.034

log 2 / log 1.034 = n

n = 20.73 years = 21 years

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