1. Analysts report that Apple’s net operating income increased by 38% in 2014, g

Question

1. Analysts report that Apple’s net operating income increased by 38% in 2014, give or take, and in 2014 this quantity was $59.3 billion. The estimated Gross World Product (GWP, the total value of all goods and services produced in the entire world) was estimated to be $77,860 billion for 2014 and growing at a rate of 3% per year. Assuming the growth in these two cases is exponential growth, and that these growth rates continue unchanged into the future, compute how many years it will take for Apple’s net operations to become equal to the total amount of business in the entire world. (I know this is a silly question for a variety of reasons, not the least of which is that continued economic growth at even a 3% annual rate is uncertain, let alone a company being able to maintain an ongoing 38% growth rate per year, but the answer might surprise you all the same. HINT: you can write down expressions for Apple’s net operating income and for the GWP as a function of t, the number of years from 2014. The question asks for the value of t when these two sums become equal.)

Explanation / Answer

Since the growth quantity was .8% which is currently $59.3 billion

and in GWP growth is 3% which is now $77860 billion.

Now suppose both values are increasing at constant rate linearly every year, then

if we calculate 59.3*1.38= 81.834

and in second year it will become 81.834*1.38 = 112.931,

now of we see 59.3*1.38^2 = 112.931

and if we talk about GWP it will become 77860*1.03^2= 82601.674 in two years (Please note that these calculations are in billion)

now if we start to keep on calculating and matching the net operating income vs GWP by bruteforce, we will get to the conclusion that in 24.56 years, both will become equal. Now let's see

59.3*(1.38)24.56= 161616.261095

and

77860*1.0324.56= 160915.040225,

which is almost equal, so we can conclude that in 25 years Apple's net income as well as GWP will becomes same.

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