Question

An economy's output grows by 2.5% annually. Calculate the number of years it takes for the economy's output to double. (Do not use the rule of 70. Calculate the exact years, round it to 2 decimal places)

A.28.25

B.28.75

C.28.07

D.28.40

E.28

Answer 1

GDP at end date = GDP at starting date (1 + growth rate of GDP)^t

Here, t = no. Of years it takes to double the GDP

GDP at starting date = Y

GDP at end date = 2Y

Therefore, 2Y = Y (1+ 0.025)^t

Or, (1.025)^t = 2

Taking logarithm on both sides we get,

t log (1.025) = log 2

Or, t = log 2 / log (1.025) = 28.07

Answer: option C