ABC company has just purchased a life truck that has a usefu

ABC company has just purchased a life truck that has a useful life of 5 years. The engineer estimates that maintenance costs for the truck during the first year will be $1,000. As the truck ages, maintenance costs are expected to increase at a rate of $300 per year over the remaining life. Assume that the maintenance costs occur at the end of each year. The firm wants to set up a maintenance account that earns 8% interest per year. All future maintenance expenses will be paid out of this account. How much does the firm have to deposit in the account now?

Solution

First year maintenance cost (A₁) = $1,000

Annual increase in maintenance cost (G) = $300

n = 5

i = 8%

So, Annual equal maintenance cost(A) = A₁ + G(A/G, i, n)

                                                    A = 1000 + 300(A/G, 8%, 5)

                                                       = 1000 + 300(1.846)

                                                       = $1553.80

It mean the company requires $1553.80 as maintenance cost for each year.

P = A(P/A, i ,n)

=1553.80(P/A, 8%, 5)

= 1553.80(3.993)

= $6204.32

Therefore, the firm have to deposit has to deposit $6204.32 in the account now