Question

PROBLEM 1. SIMPLE MODELING REVIEW PROBLEM. Suppose B(t) is the balance on your five-year car loan. B is in dollars, t is in years. B(0) = Bo is the purchase price (including tax, registration, warranties, spoiler, alloy wheels, moon roof, etc.). B(5) -0, since the loan is to be paid off in five years. Your credit history scored you a nominal annual interest rate (compounded continuously) of 5%. Even though you make your monthly payment once per month, let's assume for simplicity that you pay continuously at a rate of μ dollars per month. a. A differential equation to model the remaining balance owed is d B dt = 0.0513-M. Find M in terms of μ and explain the model in terms of rate in minus rate out. b. Identify a quantity undergoing exponential growth/decay, and use this observation to solve for B(t) in terms of μ, BO and t. c. Suppose you want a nice car, but not over-the-top awesome, such that Bo 40,000, say, which is more expensive than JC's Toyota Prius, for example. What will the monthly payment be to pay off the loan in five years? Keep this in mind when you buy your first car!

Answer 1

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Balonce - Blu) (o0 lal 2 (00 (00 (00 (0o 2 - Bo 05)

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