Question

he annual revenue-growth rates for a new tech startup during its first 4 years of operations were as follows: year 1 +50% year 2 +50% year 3: -50% year 4- -50% Rounded to the nearest tenth of one percent, the startup's 4-year Compound Annual Growth Rate was

Answer 1

Given :  annual revenue-growth rates for a new tech startup during its first 4 years of operations were as follows: year 1 +50% year 2 +50% year 3: -50% year 4- -50%

To find :  the startup's 4-year Compound Annual Growth Rate

Solution:

Let say initial Revenue  = R

After 1st year  = R + (50/100)R = 1.5R

After 2nd year = 1.5R + (50/100)1.5R = 2.25R

after 3rd Year = 2.25R - (50/100)2.25R  =  1.125R

After 4th years = 1.125R - (50/100)1.125R = 0.5625R

Compound Annual Growth Rate =  r

0.5625R =  R (1 + r/100)⁴

=>  (1 + r/100)⁴ = 0.5625

=> 1 + r/100 = 0.866

=>   r/100 = -0.134

=> r  = -13.4%

startup's 4-year Compound Annual Growth Rate was   -13.4%

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