Can someone please provide the correct solution and correct working-out? I have posted this question 3 times, and I have received different answers. Greatly Appreciated! Please ensure the answers are correct and working-out. And again thank you!!

Steven has struck a deal with his dad to buy his car when he can afford to. The car is valued at $55000 today but depreciates at a continuously compounding rate of 1% per month (i.e. 1d=e0.01 ). Steven has $9000 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=e0.01 ). (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