Discuss the similarities and differences in the graphs of unpaid balance as a function of time for 30-year mortgages of $60,000 at rates of 7 % , 10 % , and 13 % . respectively (see the figure). Include computations of the monthly payment and total interest paid in each case.
Discuss the similarities and differences in the graphs of unpaid balance as a function of time for 30-year mortgages of $60,000 at rates of 7 % , 10 % , and 13 % . respectively (see the figure). Include computations of the monthly payment and total interest paid in each case.
Solution Summary: The author explains the similarities and differences in the graphs of unpaid balance as a function of time for 30 year mortgages.
Discuss the similarities and differences in the graphs of unpaid balance as a function of time for 30-year mortgages of
$60,000
at rates of
7
%
,
10
%
,
and
13
%
. respectively (see the figure). Include computations of the monthly payment and total interest paid in each case.
EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
Chapter 3 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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