You are purchasing a home for $ 120 , 000 and are shopping for a loan. You have a total of $ 31 , 000 to put down, including the closing costs of $ 1000 and any loan fee that might be charged. Bank A offers a 10 % APR amortized over 30 years with 360 equal monthly payments. There is no loan fee. Bank B offers a 9.5 % APR amortized over 30 years with 360 equal monthly payments. There is a 3 % loan fee (i.e., a one-time up-front charge of 3 % of the loan). Which loan is better?
You are purchasing a home for $ 120 , 000 and are shopping for a loan. You have a total of $ 31 , 000 to put down, including the closing costs of $ 1000 and any loan fee that might be charged. Bank A offers a 10 % APR amortized over 30 years with 360 equal monthly payments. There is no loan fee. Bank B offers a 9.5 % APR amortized over 30 years with 360 equal monthly payments. There is a 3 % loan fee (i.e., a one-time up-front charge of 3 % of the loan). Which loan is better?
Solution Summary: The author explains that the loan from bank B is a better option for loan.
You are purchasing a home for
$
120
,
000
and are shopping for a loan. You have a total of
$
31
,
000
to put down, including the closing costs of
$
1000
and any loan fee that might be charged. Bank A offers a
10
%
APR amortized over 30 years with 360 equal monthly payments. There is no loan fee. Bank B offers a
9.5
%
APR amortized over 30 years with 360 equal monthly payments. There is a
3
%
loan fee (i.e., a one-time up-front charge of
3
%
of the loan). Which loan is better?
A factorization A = PDP 1 is not unique. For A=
7 2
-4 1
1
1
5 0
2
1
one factorization is P =
D=
and P-1
30
=
Use this information with D₁
=
to find a matrix P₁ such that
-
-1 -2
0 3
1
-
- 1
05
A-P,D,P
P1
(Type an integer or simplified fraction for each matrix element.)
Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
30 -1
-
1 0 -1
400
0
0 1
A=
3 4 3
0 1 3
040
3 1 3
0 0
4
1
0
0
003
-1 0 -1
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
A basis for the corresponding eigenspace is {
A. There is one distinct eigenvalue, λ =
B. In ascending order, the two distinct eigenvalues are λ₁
...
=
and 2
=
Bases for the corresponding eigenspaces are {
and ( ), respectively.
C. In ascending order, the three distinct eigenvalues are λ₁ =
=
12/2
=
and 3 = Bases for the corresponding eigenspaces are
{}, }, and {
respectively.
N Page
0.6.
0.4.
0.2-
-0.2-
-0.4-
-6.6
-5
W
10
Chapter 10 Solutions
Excursions in Mathematics, Loose-Leaf Edition Plus MyLab Math with Pearson eText -- 18 Week Access Card Package
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