Question

Equipment maintenance costs for manufacturing explosion-proof pressure switches are projected to be $100,000 in year 1 and increase by 4% each year through year 5.
What is the present worth of the maintenance costs at an interest rate of 10% per year, compounded quarterly for the first 3 years, if the interest rate for years 4 and 5 are 10%/year compounded monthly? (solve by hand DON'T use Excell program)

Answer 1

Maintenance cost rises by 4% each year

Interest rate = 10% per year

Rate of interest per month = (10% / 12) = 0.83% compounded per month

Rate of interest per quarter = (10% / 4) = 2.5% compounded per quarter

I am raising 12, 24, 36, 16, 20 to the below formulas because 12 means 12 times compounding in an year, 24 means 24 times compounding in 2 years, 36 means 36 times compounding in 3 years, 16 means 16 times quarterly compounding in 4 years, 20 means 20 times quarterly compounding in 5 years

Year 1: Maintenance cost in 1st year = $100,000

Present worth of maintenance cost of first year = [100,000 / (1 + 0.00833)^¹²] = 90,521.24

Year 2: Maintenance cost in 2nd year = $104,000

Present worth of maintenance cost of second year = [100,000 / (1 + 0.00833)^²⁴] = 81,940.95

Year 3: Maintenance cost in 3rd year = $108,160

Present worth of maintenance cost of third year = [100,000 / (1 + 0.00833)^³⁶] = 74,173.97

Year 4: Maintenance cost in 4th year = $112,486

Present worth of maintenance cost of forth year = [100,000 / (1 + 0.025)^¹⁶] = 67,362.49

Year 5: Maintenance cost in 5th year = $116,986

Present worth of maintenance cost of fifth year = [100,000 / (1 + 0.025)^²⁰] = 61,027.09

Sum of present value of maintenance cost is 90,521.24 + 81,940.95 + 74,173.97 + 67,362.49 + 61,027.09 = 375,025.7