A person purchased a new car for $26,200 and financed the entire amount. Suppose that the person can only afford to pay $200 per month. Assume that the payments are made at a continuous annual rate and that interest is compounded continuously at the rate of 8%. (a) Set up a differential equation that is satisfied by the amount f(t) of money owed on the car loan at time t. (b) How long will it take to pay off the car loan?

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
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Chapter1: Making Economics Decisions
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A person purchased a new car for $26,200 and financed the entire amount. Suppose that the person can only afford to pay $200 per month. Assume that the payments are made at a continuous annual rate and that interest is compounded continuously at the rate of 8%.
(a) Set up a differential equation that is satisfied by the amount f(t) of money owed on the car loan at time t.
(b) How long will it take to pay off the car loan?
...
(a) Let y = f(t) where t is the number of years after the car is purchased. Set up a differential equation that is satisfied by the amount f(t) of money owed on the car loan at time t.
%3D
y' =, y(0) =
%D
(b) It will take
years to pay off the car loan.
(Round to the nearest hundredth as needed.)
Transcribed Image Text:A person purchased a new car for $26,200 and financed the entire amount. Suppose that the person can only afford to pay $200 per month. Assume that the payments are made at a continuous annual rate and that interest is compounded continuously at the rate of 8%. (a) Set up a differential equation that is satisfied by the amount f(t) of money owed on the car loan at time t. (b) How long will it take to pay off the car loan? ... (a) Let y = f(t) where t is the number of years after the car is purchased. Set up a differential equation that is satisfied by the amount f(t) of money owed on the car loan at time t. %3D y' =, y(0) = %D (b) It will take years to pay off the car loan. (Round to the nearest hundredth as needed.)
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