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
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 = e0.0¹).
(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) Solving to equate the values in (a) and (b) to find the time when Steven can buy the car
We can equate the values in (a) and (b) to find the time when Steven can buy the car. This
gives the following equation:
55,000e - 0.01t – 0.01 Vt = 9,000e × 0.01t + 120(1 +0.01) × t + 0.01St
We can solve this equation for t to find the time when Steven can buy the car. The solution
is approximately t=100 months.
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