Question

RGDP in the United States has grown at an average annual rate of 3% in the last couple of decades. If the RGDP annual growth rate were to increase at 7%, calculate how many years earlier will it take the U.S. to double its RGDP when comparing a 7% growth rate to a 3% growth rate.
It will take the U.S. _____ years earlier to double its RGDP. Round up your answer to the second decimal.

Answer 1

Explanation:

i=interest rate

X=current rate

2X = double current rate

n = number of years

Calculate time it takes to double at 3%:

2X = X(1+i)^n

simplify by cancelling out X

(1+i)^n = 2

substitute i = 3%

(1.03)^n =2

take log

n*log(1.03)  = log(2)

n = log(2)/log(1.03) = 0.6931/0.02956 = 23.45 years

Similarly, for growth rate of 7%,

n = log(2)/log(1.07) = 0.6931 / 0.06766 = 10.24 years

So the difference is 23.45-10.24 = 13.21 years (to the hundredth)  sooner