Question

A Highway Department expects the cost of maintenance for a piece of heavy construction equipment to be $5,000 in year one, and to be $4,500 in year 2 , and to decrease annually by $500 through year 10. At an interest rate of 10% per year, determine the present worth (i.e. PV) of the whole 10 years of maintenance costs. Initial questions to be answered:

A) What is the A in period one?
B) What is the G (change) between periods?
C) What is the number of periods ( 1 through n ) of the gradient cash flow?
D) What is the interest rate per period (in percent)? Note: Use only the Interest Factor Tables (in the back of the book) to solve this problem. Show your (step-by-step) work (below), documenting each step of solving this problem. [Hint: Don't skip steps.] Put a "box" around your final answer.

Answer 1

To calculate the present worth of 10 years of maintenance costs, you need to determine the present value of each year's maintenance cost and then sum them up. The A in period one is $5,000, the G (change) between periods is $500, the number of periods is 10, and the interest rate per period is 10%.

Step-by-step explanation:

In order to calculate the present worth of the whole 10 years of maintenance costs, we need to determine the present value (PV) of each year's maintenance cost and then sum them up.

A) The A in period one is $5,000.

B) The G (change) between periods is $500.

C) The number of periods (1 through n) of the gradient cash flow is 10.

D) The interest rate per period is 10%.

To calculate the present value, we can use the formula PV = A * (1 - (1 + i)^(-n)) / i + G * (1 - (1 + i)^(-n)) / (i * (1 + i)^n), where PV is the present value, A is the annual maintenance cost in period one, i is the interest rate per period, n is the number of periods, and G is the change between periods.