Homework Help is Here – Start Your Trial Now!
Business
Economics
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
See similar textbooks
icon
Related questions
Question

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 =
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

I heard that t = 66 months, is this true or false?

Solution
Bartleby Expert
SEE SOLUTION
Follow-up Question

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

Solution
Bartleby Expert
SEE SOLUTION
Knowledge Booster
Assets
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS