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

Find the periodic payment R required to amortize a loan
of P dollars over t years with interest charged
at the rate of r%/year compounded m times a year.
(Round your answer to the nearest cent.)
P = 50,000, r = 4, t = 20, m
= 6
P = 80,000, r = 9.5, t = 20,
m = 12
S = 50,000, r = 6, t = 7, m
= 6

5) The economy has an aggregate production function
fN=15N-12N2 , where N is labor
input. Labor supply is given by
NsWP=-5+3WP ,
where W is the money wage and P is the price level. Desired
consumption depends on real income, Y, and can be written as
CdY=10+0.7Y . Given real
interest rate, r, the desired investment is
Idr=30-200r . The real money
demand is characterized by LY,r=10+Y-200r . Government spending, G,
and nominal money stock, M, is given as G=0...

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