A company is planning to buy a machine costing $$25,000.$ It is estimated that the machine

will save $$3,000$ per year over the next $12$ years after which it will be sold as salvage for

$$2000.$ If the company requires a $6\%$ return on investment to justify the purchase, is it

worth buying the machine? Ignore all other accounting or tax considerations and use

finite geometric series. The money is spent at the beginning of year one. The $$3000$ per year

savings accrues at the end of each year one thru twelve and needs to be discounted at $6\%$

back to the beginning of year one to be comparable to the initial investment $($this gives the

net present value of the savings$).$ Don't forget that the $$2000$ needs to be brought all the

way back from the end of year twelve to the beginning of year one. The overall net present

value is the discounted value of the savings plus the discounted value of the salvage value

minus the outlay for the machine at the beginning of the life of the investment.