Question

Q1- The cost of maintaining a piece of construction equipment increases at a constant rate of AED 80 per month over its 16 year life. This year’s cost (end of year 1) is expected to be AED 7500. Determine

1. the cost at the end of year 13
2. the Present Worth of the maintenance costs at an interest rate of 9%.

Answer 1

Cost at the end of year 1 = AED 7,500

Maintenance cost increases by AED 80 per month

Each year the maintenance cost increases by $ 80 × 12 = 960

End of 2nd year cost = 7,500 + 960 × 1 = 8460

Year 3 = 7,500 + 960×2 = 9,420

Like wise in year 13 = 7,500 + 960 × 12 = 19,020

Cost at the end of year 13 = $ 19,020.

b. We are required to calculate the present worth of the cost at a rate of 9% for 16 years.

Cost at the end of year 1 = $ 7,500

Each year maintenance cost increases by $ 960

The present worth of the maintenance cost will be

PW = 7,500(P/A,9%,16) + 960(P/G,9%,16)

The value of the factors we can calculate from the factor table

PW = 7,500 × 8.3125 + 960 × 47.5849

=> PW = $ 108,025.70

I have solved it using the annual value because the amount is mentioned in terms of cost at the end of year 1. So instead of calculating it on monthly basis i have solved it using annual end year cost.

Please contact of you feel we are required to solve it on monthly basis the present worth using monthly increase will be $ 1,268,012. Please let me know if you have any query will be obliged to you for your generous support. Your help mean a lot to me, please help. Thank you. Please help me.