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 12% 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

Total amount to be invested today = $1,706.432

Explanation:

The first maintenance cost would occur a year from now, then the Present value will be equal to:

PV = 1,000 * 1.12^ (-1)

PV = 892.857

The rest of the maintenance cost represents an annuity.

We will determine the PV of the annuity of $300 discounted at 12% per annum starting in year 2

PV = A * 1 - (1+r) ^ (-n)

A - 300, r = 12%, n = 4

PV in year 1 = 300 * 1 - (1.12) ^ (-4) = 911.204804

PV in year 0 = F * (1+r) ^ (-n)

= 911.204804 * 1.12^ (-1) = 813.57

Total amount to be invested today = 813.57 + 892.85=1706.43

Total amount to be invested today = $1,706.432