If an economy is growing at 4% a year, how long will it take for its...

Question

Question

If an economy is growing at 4% a year, how long will it take for its income to double?

Answer 1

Answer #1

Growth rate = 4% = 0.04

Let.

Present Income = Y

So Double Income = 2Y

Time for it to double = n years

From Growth formula we know

$Future Income = Present Income 1 + Growth rate)$

So,

2Y = Y(1 + 0.04)ⁿ

2 = (1.04)ⁿ

Taking log on both sides :

log(2) = n * log(1.04)

n = log(2)/log(1.04) = 0.301/0.017

n = 17.7 years ~ 18 years

So, It will take around 18 years for the economy to double its income at growth of 4% per year.

Answer 2

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