The Monthly Mortgage Payment in Dollars, P, for a House

question 127

Essay

The monthly mortgage payment in dollars, P, for a house is a function of three variables P = f(A, r, N), where A is the amount borrowed in dollars, r is the interest rate, and N is the number of years before the mortgage is paid off.It is given that: $$\begin{array} { l l l } f ( 100000,7,20 ) = 775.29 , & f ( 100000,8,20 ) = 836.44 , & f ( 100000,7,25 ) = 706.77 \\f ( 120000,7,20 ) = 930.35 , & f ( 120000,8,20 ) = 1003.72 , & f ( 120000,7,25 ) = 848.13\end{array}$$ Estimate the value of $$\left. \frac { \partial f } { \partial r } \right| _ { ( 100000,7,20 ) }$$

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Definitions:

Psychoanalytic Method

A clinical method for treating psychopathology, originating from Freudian theory, that involves exploring unconscious conflicts, desires, and experiences.

Bethlehem Hospital

An historical institution in London, known as Bedlam, originally a hospital dedicated to mental illness treatment.

Mentally Ill Persons

Individuals who experience significant disruptions in their thinking, feeling, mood, or behavior, associated with distress or impaired functioning.

Psychoanalysis

An insight therapy based on the theory of Freud, emphasizing the revealing of unconscious conflicts; Freud’s term for both the theory of personality and the therapy based on it.