Question

John is a very​ cost-conscious investor. His rule of thumb is that it costs ​300$ per​ year, starting in the first year of vehicle life to maintain an automobile. This expense increases by ​300$ each year over the life of the car. John is now considering the purchase of a 6 ​-year old car with 50000 miles on it for ​$8000. How much money will John have to set aside now to pay for maintenance​ (as a lump​ sum) if he keeps this car for 8 ​years? John's interest rate is 4​% per year.

John will have to set aside how much to pay for maintenance?

Answer 1

John needs to set aside approximately $12,004.85 to pay for maintenance as a lump sum.

Step-by-step explanation:

Calculate the total annual maintenance cost for each year:

Year Annual Maintenance Cost

1 $300

2 $600

3 $900

4 $1,200

5 $1,500

6 $1,800

7 $2,100

8 $2,400

Find the present value (PV) of each annual cost using the formula:

PV = Future Value / (1 + Interest Rate)^Year

Sum the present values of all annual costs:

Total PV of Maintenance Costs ≈ $3,159.33 + $2,682.22 + $2,281.96 + $1,941.53 + $1,655.59 + $1,423.49 + $1,234.89 + $1,082.74 ≈ $12,004.85

Therefore, John needs to set aside approximately $12,004.85 now to cover the total future maintenance costs in a single lump sum. This takes into account the increasing cost over time and the discounting effect of his 4% annual interest rate.