Interpretation of A Derivative?

Question

1.Suppose P(t) is the monthly payment, in dollars, on a mortgage
which will take t years to pay off. What is the practical meaning of
P'(t) (derivative of P(t)) and what is it's sign?

Iam a little confused about questions that answer questions like this. Can someone answer me that question so I can clearly understand more.

Answer 1

P'(t) is the rate at which your morgatge payment is changing. In this case, the sign would be negative, since the amount of principal remaining decreases continually, and therefore so does the amount of interest, and by extension the amount of your morgatge payment.

Answer 2

Derivative signifies the rate of change of anything.
Suppose you have a million dollars and no income. Then you are making steady payments out of this at the rate of five dollars per week. Now what happens to your money ? It is going down at the rate of five dollars per week. So the derivatives of your money with respect to time is =negative five (and the unit in this case is dollars per week).The rate is negative because your money balance is reducing.
On the other hand if you are not making any payments, you are earning Dollars 1000 per week. Now the derivative of your money with respect to time is positive 1000. The derivative may not be constant. Because, when you are making payments without any earnings, may be you want to slow down the payments when your balance is low.