please show all work and equations used, thanks!

21. The maintenance cost of a certain machine is zero the first year and increas by $200 per year for each year thereafter. The machine cost $2,000 and nas salvage value at any time. Its annual operating cost is $1,000 per year.! interest rate is 10%, what life will result in minimum AE(i) cost? Solve by trial and error, showing vearly costs in tabular form