Question

The monthly payment for a home loan is given by a function f(P,r,N)f(P,r,N) where PP is the principal (the initial size of the loan), rr the interest rate, and NN the length of the loan in months. Interest rates are expressed as a decimal: A % interest rate is denoted by r=0.03. If P=150000,r=0.03 and N=336N=336(a 28-year loan), then the monthly payment is f(150000,0.03,336)=1921. Furthermore, with these values we have

∂f/∂P=0.0057,∂f/∂r=9727,∂f/∂N=−1.6013

Estimate:

(a) The change in monthly payment per 2000 increase in loan principal:
Δf≈ dollars
(b) The change in monthly payment if the interest rate changes from r=0.03 to r=0.015:
Δf≈ dollars
(c) The change in monthly payment if the length of the loan changes from 2828 to 3232 years:
Δf≈Δf≈ dollars

Answer 1