Question 2 Steven has struck a deal with his dad to buy his car when he can afford to. The car is valued at $55 000 today but depreciates at a continuously compounding rate of 1% per month (i.e. 1 — d = e−0.01). Steven has $9 000 in a bank account and plans to add $120 each month end. The bank pays interest at a continuously compounding rate of 1% per month (i.e. 1 + r = 0.0¹). (a) Formulate the value of the car as a finite difference equation and solve by calculating the Complementary Function and Particular Solution. (b) Formulate Steven's Savings amount in a similar way and solve. (c) Solve to equate the values in (a) and (b) to find the time when Steven can buy the car.

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