Car Replacement

I just purchased (at time 0), a new car for $12,000. The cost of maintaining a car during a year depends on its age at the beginning of the year. To avoid the high maintenance costs associated with an older car, I may trade in my car and purchase a new car. The price I receive on a trade-in depends on the age of the car at the time of trade-in. Assume that at any time it costs $12000 to buy a new car. The goal is to minimize the net cost incurred during the next five years.
Age of Car Annual Maintenance Cost Trade in Price
0 $2000
1 $4000 $7000
2 $5000 $6000
3 $9000 $2000
4 $12000 $1000
5 $0

by Cliff Stein and used with permission.