(1 point) The monthly payment for a home loan is given by a function f(P, r, N)

Question

(1 point) The monthly payment for a home loan is given by a function f(P, r, N) where P is the principal (the initial size of the loan), r the interest rate, and N the length of the loan in months. Interest rates are expressed as a decimal: A % interest rate is denoted by r = 0.04. If P = 200000, r = 0.04, and 336(a 28-year loan), then the monthly payment is f(200000, 0.04, 336-1900. Furthermore, with these values we have af 01=0.0053, a af ON of 1.5304 Estimate: (a) The change in monthly payment per 1000 increase in loan principal: (b) The change in monthly payment if the interest rate changes from 0.04 to 0.035; (c) The change in monthly payment if the length of the loan changes from 28 to 27 years: E dollars E dollars dollars

Explanation / Answer

deltaf = fP(P - P1) + fr(r - r1) + fN(n - n1)
where fP , fr and fN are the partial derivative values given
and (P1,r1,n1) = (200000 , 0.04 , 336)

So deltaf = 0.0053(1000) + 0 + 0
0 and 0 cuz r and n aint changin'

deltaf = 5.3 dollars ---> ANS

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deltaf = fP(P - P1) + fr(r - r1) + fN(n - n1)
deltaf = 0 + 6918(0.035 - 0.04) + 0

deltaf = -34.59 dollars ----> AN?S

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deltaf = fP(P - P1) + fr(r - r1) + fN(n - n1)

deltaf = 0 + 0 + -1.5304(27 - 28)

deltaf = 1.5304 dollars ---> ANS

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