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
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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is my part (c) correct?

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.

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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