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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 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

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 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

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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is my part (c) correct?

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.
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.
(c) Solve to equate the values in (a) and (b) to find the time when Steven can buy the car. 1 Explanation: To find the time when Steven can buy the car, we need to solve the equation V(t) = S(t). Substituting the expressions we derived earlier: -0.01t $55,000 × e Simplifying the equation: -0.01t 100xet+In (210)_120 $55,000 × e = et+In (210)_120 0.01 0.01 $55, 000 × e 100 × et+In (210) 12,000 Using a numerical solver, we can find an approximate solution for t: t≈ 12.964 Therefore, the approximate time when Steven can buy the car ist≈ 12.964 months. -0.01t =
Transcribed Image Text:(c) Solve to equate the values in (a) and (b) to find the time when Steven can buy the car. 1 Explanation: To find the time when Steven can buy the car, we need to solve the equation V(t) = S(t). Substituting the expressions we derived earlier: -0.01t $55,000 × e Simplifying the equation: -0.01t 100xet+In (210)_120 $55,000 × e = et+In (210)_120 0.01 0.01 $55, 000 × e 100 × et+In (210) 12,000 Using a numerical solver, we can find an approximate solution for t: t≈ 12.964 Therefore, the approximate time when Steven can buy the car ist≈ 12.964 months. -0.01t =
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I heard that t = 66 months, is this true or false?

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So my t = 12.964 is wrong? How can I be sure that t = 90? Greatly Appreciated!!

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