Question

1. Assume that China’s GDP grows at a rate of 8% annually, and the USA’s at 2.5%. Suppose that in 2010 the GDP of the two countries were 6 trillion and 14 trillion respectively. At these growth rates, in what year can we expect to see China’s GDP equal that of the USA?

   (a) 2054 (b) 2026

   (c) 2020 (d) 2042 (e) 2035

Answer 1

Answer

The correct answer is (b) 2026

Future Value is given by:

FV = P(1 + r)ⁿ

where P = Initial Value of GDP , FV = Future Value of GDP , n = Time and r = growth rate

We want FV for China and US to be equal.

FOR US:

P = Initial Value of GDP = 14 trillion , FV = Future Value of GDP , n = Time and r = growth rate = 2.5% = 0.025

=. FV = 14 trillion*(1 + 0.025)ⁿ

FOR CHINA

P = Initial Value of GDP = 6 trillion , FV = Future Value of GDP , n = Time and r = growth rate = 8% = 0.08

=. FV = 6 trillion*(1 + 0.08)ⁿ

We have to Find n such that FV of Both china and US are equal

=> 14 trillion*(1 + 0.025)ⁿ = 6 trillion*(1 + 0.08)ⁿ

=>14/6 = (1 + 0.08)ⁿ/(1 + 0.025)ⁿ

=> 7/3 = (1.08/1.025)ⁿ

Taking log on both sides we get

log(7/3) = n*log(1.08/1.025)

Note that log(a^b) = b*log(a)

=> n = log(7/3) / [log(1.08/1.025)] = 16.

Thus year at which we expect to see China’s GDP equal that of the USA is 2010 + 16 = 2026.

Hence, the correct answer is (b) 2026