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Inquisitio September 6th, 2016 02:18 PM

When will the revenue even ?

I have to solve this super easy task but to be honest I have no idea how. This isn't exactly finance but had nowhere else to post so I thought I'd give it a try here.

Company A has a yearly revenue of 300000 and it increases by 5% a year.
Company B has a yearly revenue of 200000 and it increases by 7% a year.

How long untill the revenue is even and how much will both companies earn at that point ?


romsek September 6th, 2016 04:17 PM

Assuming the interest compounds annually we have

$A = 300000(1+0.05)^n$

$B = 200000(1+0.07)^n$

where $n$ is in years

setting these equal to one another we get


$\dfrac 3 2 = \left(\dfrac{1.07}{1.05}\right)^n$

$\log(1.5) = n\left(\log(1.07) - \log(1.05)\right)$

$n = \dfrac{\log(1.5)}{\log(1.07) - \log(1.05)} \approx 21.49yr$

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