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 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.
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 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I had trouble doing this question, I sincerely ask you to please solve this problem, please provide correct and concise working-out. Please also mainly focus on part (c) as well. Greatly Appreciated!!
Transcribed Image Text: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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