You're thinking of buying a car to travel around in$,$ rather than paying $$2,563$ at the end of every year to use the train. You can buy an old second hand car for $$7,000$ now $($t$=0),$ and sell it after $8$ years for $$6,500($t$=8).$ You estimate that the car will cost $$2,500$ per year in fuel, insurance, registration and maintenance, paid in arrears, so there will be $8$ payments from t$=1$ to t$=8$ inclusive. The required return is $4\%$ pa$.$ Select the most correct statement. The equivalent annual cost $($EAC$)$ of the car is: a$.$

$$2,385$ so the car is cheaper than the train.

b$.$

$$2,834$ so the train is cheaper than the car.

c$.$

$$3,179$ so the train is cheaper than the car.

d$.$

$$23,832$ so the train is cheaper than the car.

e$.$

$$70,857$ so the train is cheaper than the car.