Question

Connect Problem CP 22-4 (algo) Suppose that a developing country currently has a per capita GDP of $1,150 and has a goal to double its average standard of living in 14 years What will be the approximate annual economic growth rate required for this country to attain its goal? (Hint Use the Rule of 70.) Instructions: Round your answer to 2 decimal places. percent

Answer 1

Present per capita GDP = $1,150

Double its average standard of living in 14 years

What should be the approximate annual economic growth rate required to attain the goal?

Using the Rule of 70

Number of years to double = 70 ÷ Annual growth rate

14 years =70 ÷ Annual Growth rate (%)

14x = 70 (let x is the growth rate)

X = 70 / 14 = 5

Or X = 5%

Approximate annual economic growth rate required will be 5% to attain the goal.

Verification

F = P (F/P, 5%, 14)

F = $1,150 (1.980) = $2,277 (Rounding to nearest value $2,300)

Answer 2

SOLUTION :

It is rule 72 and not rule 70.

As per rule 72, for doubling any growth ,

time required = 72 / growth rate in  %

Time required in the given case to double the economic growth is 14 years.

So,

Growth rate required in (%) 

= 72 / time required to double the growth

= 72/ 14

= 5.014 % 

= 5.01 % approx. (ANSWER).

Check :

GDP in Y14 / Current GDP = (1 + 5.01/100)^ 14 = 1.983 = 2 approx. ( Answer is ok) .