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.

(a) Is $\partial P /\partial t$ positive or negative? ? positive negative
Suppose that your bank tells you that the magnitude of $\partial P /\partial t$ is 15.
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.)

(b) Is $\partial P /\partial r$ positive or negative? ? positive negative
Suppose that your bank tells you that the magnitude of $\partial P /\partial r$ is 25.
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.

Solution: