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September 6th, 2016, 01:18 PM  #1 
Newbie Joined: Sep 2016 From: Poland Posts: 1 Thanks: 0  When will the revenue even ?
Hey, 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 ? Cheers! 
September 6th, 2016, 03:17 PM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 623 Thanks: 331 
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 $300000(1+0.05)^n=200000(1+0.07)^n$ $\dfrac 3 2 = \left(\dfrac{1.07}{1.05}\right)^n$ $\log(1.5) = n\left(\log(1.07)  \log(1.05)\right)$ $n = \dfrac{\log(1.5)}{\log(1.07)  \log(1.05)} \approx 21.49yr$ 

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