Math Help - need help please!

Machine A can be bought for $15,000, but machine B, the automated model, will cost $40,000 to buy and install. The automated machine will reduce annual cost by $5743.50 over machine A. Either machine will have a service life of seven years. The rate of return on the extra investment required by buy machine B is

Originally Posted by JAMESANANE

Machine A can be bought for $15,000, but machine B, the automated model, will cost $40,000 to buy and install. The automated machine will reduce annual cost by $5743.50 over machine A. Either machine will have a service life of seven years. The rate of return on the extra investment required by buy machine B is

Someone with more business saavy might approach this differently, but here goes:

The $40,000 purchase will more than pay for itself in 7 years considering the annual reduction in operating costs (7 X $5,743.50 = $40,204.50).

The return on investment (ROI) given just that information would be


If you figured from just the extra investment made ($40,000-$15,000=$25,000), then the ROI would be

1. The rate of return on the extra investment is merely the extra profit you get from it each year divided by the additional initial investment. So that's 5743/25,000 = 23%

2. The formula for compounding interest is:



So here you have

or


Now solve for n. The way to do that is using logarithms. Take the log of both sides:



Recall from highschool that , so you have

, and hence