A person purchased a house 10 years ago for $160,000 . The house was financed by paying 20 % down and signing a 30-year mortgage at 7.75 % on the unpaid balance. Equal monthly payments were made to amortize the loan over a 30 -year period. The owner now (after the 120 th payment) wishes to refinance the house due to a need for additional cash. If the loan company agrees to a new 30-year mortgage of 80 % of the new appraised value of the house, which is $225,000 , how much cash (to the nearest dollar) will the owner receive after repaying the balance of the original mortgage?
A person purchased a house 10 years ago for $160,000 . The house was financed by paying 20 % down and signing a 30-year mortgage at 7.75 % on the unpaid balance. Equal monthly payments were made to amortize the loan over a 30 -year period. The owner now (after the 120 th payment) wishes to refinance the house due to a need for additional cash. If the loan company agrees to a new 30-year mortgage of 80 % of the new appraised value of the house, which is $225,000 , how much cash (to the nearest dollar) will the owner receive after repaying the balance of the original mortgage?
Solution Summary: The author calculates the amount of cash received by the owner after paying the balance of the original mortgage.
A person purchased a house
10
years ago for
$160,000
. The house was financed by paying
20
%
down and signing a 30-year mortgage at
7.75
%
on the unpaid balance. Equal monthly payments were made to amortize the loan over a
30
-year period. The owner now (after the
120
th
payment) wishes to refinance the house due to a need for additional cash. If the loan company agrees to a new 30-year mortgage of
80
%
of the new appraised value of the house, which is
$225,000
, how much cash (to the nearest dollar) will the owner receive after repaying the balance of the original mortgage?
Refer to page 145 for problems on constrained optimization.
Instructions:
•
Solve an optimization problem with constraints using the method of Lagrange multipliers.
•
•
Interpret the significance of the Lagrange multipliers in the given context.
Discuss the applications of this method in machine learning or operations research.
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Give an example of a graph with at least 3 vertices that has exactly 2 automorphisms(one of which is necessarily the identity automorphism). Prove that your example iscorrect.
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