Is my part (c) correct? (c) Equating the values of the car and Steven's savings:To find the time when Steven can buy the car, we need to solve the equation:V(t) = S(t)Substituting the expressions we found:55,0000.01LThis equation can't be solved analytically, so let's use numerical methods to approximate the value of tOne common numerical method is the Newton-Raphson method. We start by rearranging theequation to have zero on one side:55,000-120€ - 9,000=0Now, let's define a function f(t) = 55,000e011120t -9,000. We want to find the value of twhere fit) is equal to zero.We can start with an initial guess fort, such as t=1, and then use the Newton-Raphson method toiteratively refine our approximation.The Newton-Raphson iteration formula is given by:[(L₂)P(1₂)= 120€ +9,000t+=t₂Where t, is the current approximation, f(ta) is the value of the function at to and f'(t.) is thederivative of the function at tLet's calculate the derivative of fit) first.f'(t)=-550e--120t₁ = to= 1Now, we can start the iteration process:Initial guess: t, =1[(4)P(4)55,041,201-9,00055.01.20t₂ = t₁-Performing the calculations:t₁2.376We continue this process by t, back into the equation:[(4)P(4)₂ 2.381We repeat these iterations until we reach a desired level of accuracy. Let's continue the calculations:t2.381₁2.381We can see that the value of t stabilizes around t 2.381.Therefore, the approximate time when Steven can buy the car ist & 2.381 months. Question 2Steven 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 of1% 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 bankpays 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 calculatingthe 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 thecar.

Current value of Car = 55000 Depreciation per month = 1% Steven's bank current balance =…

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 = e0.01). (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 = 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 = e0.01). (a) Formulate the value of the car as a finite difference equation and solve by calculating

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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