Consider a Function of Three Variables $P = f ( A , r , N )$

question 70

Essay

Consider a function of three variables $P = f ( A , r , N )$ , where $P$ is the monthly mortgage payment in dollars, $A$ is the amount borrowed in dollars, $r$ is the annual interest rate, and $N$ is the number of years before the mortgage is paid off.(a) Suppose $f ( 180,000,6,30 ) = 1080$ . What does this tell you in financial terms?
(b) Suppose $\frac { \delta f } { \delta r } ( 180,000,6,30 ) = 115.73$ . What does this tell you in financial terms?
(c) Suppose $\frac { \delta f } { \delta N } ( 180,000,6,30 ) = - 12.86$ . What does this tell you in financial terms?

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Definitions:

Pull-in Current

The current required to bring an electric motor up to full operational speed from a standstill.

Dropout Current

The minimum current level at which a device, like a relay, deactivates or returns to its "off" state.

Magnetic Lines

Invisible lines of magnetic force that emanate from magnetic fields, showing the direction a magnetic force acts.

Flux

Flux, in the context of electromagnetism, refers to the rate of flow of a property per unit area, such as the magnetic field lines per unit area in a magnetic circuit.