The monthly payment for a home loan is given by a functionf(p, r, n),where p is the principal (the initial size of the loan), r the interest rate expressed as a decimal (a 6% interest rate is denoted by r = 0.06), and n the length of the loan in months. if p = $100,000, r = 0.06, and n = 240 (a 20-year loan), then the monthly payment is f(100,000, 0.06, 240) = 716.43. furthermore, with these values, we have? f? p= 0.0072,? f? r= 5,769,? f? n= ? 1.5467.estimate the following values.(a) the change in monthly payment per $1,000 increase in loan principal.? f = $) the change in monthly payment if the interest rate increases to r = 6.5%.? f = $) the change in monthly payment if the length of the loan increases to 24 years.? f = $

a) a change in the principal of 100 dollar will increase the monthly payment for 7.164 dollars

b) and increase inthe rate to 6.5% from 6% will increase the monthly payment for $   29.14

c) an increase inthe lenght of the loan to 24 years will decrease the payment per month by 60.45 dollars

Explanation:

We calcualte the annuity of 1,000 dollar under the same conditions:

PV  $1,000.00

time240

rate0.005 (6% annual divide into 12 months per year)

C  $ 7.164

Then, the change if rate increase to 6.5%

C of 6.50%  $ 745.573

C of 6.00%       $ 716.43

Difference:      $   29.14

last, if n = 24 years = 24 x 12 = 288

C of 24 years  $ 655.98

C of 20 years  $  716.43

Differnece       $  (60.45)

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