(A) A family has an $85,000 , 30 -year mortgage at 9.6 % compounded monthly. Show that the monthly payments are $720 .94 . (B) Explain why the equation y = 720.94 1 − 1.008 − 12 30 − x 0.008 gives the unpaid balance of the loan after x years. (C) Find the unpaid balance after 5 years, after 10 years, and after 15 years. (D) When does the unpaid balance drop below half of the original $85,000 ? (E) Solve part (D) using graphical approximation techniques on a graphing calculator (see Fig. 3).
(A) A family has an $85,000 , 30 -year mortgage at 9.6 % compounded monthly. Show that the monthly payments are $720 .94 . (B) Explain why the equation y = 720.94 1 − 1.008 − 12 30 − x 0.008 gives the unpaid balance of the loan after x years. (C) Find the unpaid balance after 5 years, after 10 years, and after 15 years. (D) When does the unpaid balance drop below half of the original $85,000 ? (E) Solve part (D) using graphical approximation techniques on a graphing calculator (see Fig. 3).
Q3*) Consider the integral
I
Yn, Y₁, Y2, . . ., Y'n) dã,
[F(x, Y 1, Y2, · · Yng)
= -
where y1, 2, ...y are dependent variables, dependent on x. If F is not explicitly dependent on x, deduce
the equivalent of the Beltrami identity. Optional: Give an example of a function F(y1, Y2, Y₁, y2), and write
down the Euler-Lagrange equations and Beltrami Identity for your example. Does having this Beltrami Identity
help solve the problem?
Write an integral that is approximated by the following Riemann sum. Substitute a
into the Riemann sum below where a is the last non-zero digit of your banner ID.
You do not need to evaluate the integral.
2000
(10
1
((10-a) +0.001) (0.001)
Solve the following problem over the interval from x=0 to 1 using a step
size of 0.25 where y(0)= 1.
dy
=
dt
(1+4t)√√y
(a) Euler's method. (b) Heun's method
Chapter 3 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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