Draw a decision tree for this problem. To simplify it$,$ look at the situation on a yearly basis for $3$ years. If you buy the new car, you can

anticipate cash outflows of $12$ X $$201\mathrm{.}85=$ $$2,422\mathrm{.}20$ plus maintenance

costs. For the used car, some of the repair costs are known $($immediate repairs this year, tires next year$),$ but we must model the uncertainty associated with the rest. In addition to the known repairs, assume that in each year there is a $20\%$ chance that these uncertain repairs will be $$500,$ a $20\%$ chance they will be $$2,500,$ and a $60\%$ chance they will be $$1,500.($Hint: You need three chance nodes: one for each year!$)$

To even the comparison of the two cars, we must also consider their values after $3$ years. If you buy the new car, it will be worth approximately $$8,000,$ and you will still owe $$4,374.$ Thus, its net salvage value will be $$3,626.$ On the other hand, you would own the used car free and clear $($assuming you can keep up with the repair bills!$),$ and it would be worth approximately $$2,000.$

Include all of the probabilities and cash flows $($outflows until the last branch, then an inflow to represent the car's salvage value$)$ in your

$3\mathrm{.}26$

decision tree. Calculate the net values at the ends of the branches.