Choices: positive or negative Your monthly car payment in dollars is P = f(P_0,

Question

Choices: positive or negative

Your monthly car payment in dollars is P = f(P_0, t, r), where $P_0 is the amount you borrowed, t is the number of months it takes to pay off the loan, and r percent is the interest rate. Is dP/dt positive or negative? Suppose that your bank tells you that the magnitude of dP/dt is 20. What are the units of this value? (For this problem, write our your units in full, writing dollars for $, months for months, percent for %, etc. Note that fractional units generally have a plural numerator and singular denominator.) Is dP/dr positive or negative? Suppose that your bank tells you that the magnitude of dP/dr is 5. What are the units of this value? (For this problem, write our your units in full, writing dollars for $, months for months, percent for %, etc. Note that fractional units generally have a plural numerator and singular denominator.) For both parts of this problem, be sure you can explain what the practical meanings of the partial derivatives are.

Explanation / Answer

a) p/t is negative, because as the number of periods increases , monthly payment decreases

units of p/t are dollars/month

b) p/r is posittive, because as the interest rate increases , monthly payment increases

units of p/r are dollars/%

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