An engineer has recently purchased a new piece of equipment to use in analyzing geological formations. The equipment has no maintenance costs the first year due to a one year's free maintenance warranty. In the second year, it is expected to cost $250 to maintain the equipment and in subsequent years the cost of maintenance will increase by $50 per year. Approximately what amount must be set aside now at 7% interest to pay the cost of maintaining the equipment over the first twelve (12) years of ownership

there are two out flows:

1) the payment of maintenance $250 From year 2 to 12

2) The increase in maintenance cost $50 from year 3 to 12

Calculate the present value using annuity formula for both cash outflows

1)

total payments = 11 (form year 2 to 12)

payment = $250

Rate = 7%

present value = P=R (1 - (1+i) ^n) / i

P=250 (1 - (1+i) ^-11) / 7%

P=250 * 0.5249 / 7%

P=250 * 7.4986

P=1874.67

2)

total payments = 10 (form year 3 to 12)

payment = $50

Rate = 7%

present value = P=R (1 - (1+i) ^n) / i

P=50 (1 - (1+i) ^-10) / 7%

P=50 * 0.4916 / 7%

P=50 * 7.0235

P=351.1791

Total payment that should be set side = 1874.67+351.1791 = 2225.848