You are currently driving an older model car. As an approximation, you expect that the annual maintenance costs $($paid at the end of each year$)$ will be i$.$$$1,000$ for the coming year, $($paid at t $=1$ if driven in year $1)$ ii$.$$$1,500$ for the second year $($paid at t $=2$ if driven in year $2)$ iii.$$2,500$ for the third year $($paid at t $=3$ if driven in year $3)$ The car currently has a market value of $$2,000$ and you expect this to fall to $$1,000$ at the end of year $1,$ to $$500$at the end of year $2,$ and to be zero at the end of year $3$ when the car will stop running and become junk $($take to the dump $-$ $$0$ cost$).$ You find that a newer model replacement vehicle currently costs $$8,000$ to purchase and is expected to last $7$ years, with maintenance costs of $$200$ at the end of its first year of operation, with subsequent maintenance costs growing by $50\%$ per year thereafter through its $7$thyear of operation whereafter the car will stop running and become junk and need to be replaced with a similar newer model with exactly the same costs. Assume all of these costs are in real terms and that future replacement cars with the same real costs will be the replacementsin any year into the future. Assume further that a reasonable real discount rate for this problem is $6\%$ per year.