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 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). -
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Can somebody complete the workout on part (c)?

Transcribed Image Text:(c) Equating the values in (a) and (b) to find the time when Steven can buy the car:
To find the time when Steven can buy the car, we equate the values of V(t) and S(t) and solve for t:
V(t) = S(t)
(Ae^(kt) + $55,000) = (Be^(pt) + $9,000)

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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