Rebecca is purchasing a house for $210,000, with a 15-year fixed-rate mortgage at 4.5% interest. She has made a 5% down payment.
2 answers:
Solution:
Cost of the house with a 15-year fixed-rate mortgage at 4.5% interest= $ 210,000
Actual cost of house = $ 198,000
Down payment made by Rebecca
=5 % of $ 198,000
$
Local tax paid by Rebecca = 4.5 % of $ 198,000
$
Homeowners insurance per year made by Rebecca= $ 840
Total interest paid = $ 210,000 - $ 198,000
= $ 12,000
She will pay this money in 15-years at fixed-rate mortgage of 4.5% interest.
Money that Rebecca will pay at the end of each year
Mortgage rate = (4.5 % of 198,000) Per yearly
$ yearly
Total money that Rebecca has to pay after each passing year = 9,900+8,910+840+800+8910=$ 29,360
Amount that Rebecca has to pay monthly=
$
Option (A) $2437.20 appears appropriate.
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There are no algebraic methods for finding solutions to a general mix of exponential and polynomial terms. A graphing calculator can be helpful.
This equation has 3 real solutions, approximately ...
x ∈ {-0.802246431546, 1.51677641228, 7.17475582739}
_____
In the folder "iteration for solutions" is an equation for Newton's method iteration, essentially, ...
g(x) = x -f(x)/f'(x)
where f(x) is defined as shown in the picture.
Many graphing calculators can compute a numerical derivative, so you can essentially write the formula in this form without having to do the derivative-taking yourself. This calculator is nicely interactive, so the iteration result is produced at the same time the argument for g(x) is entered. Essentially, you write the answer by copying the answer using the 4-digit zero-crossing values shown on the graph as the iteration starting point.
This equation has 3 real solutions, approximately ...
x ∈ {-0.802246431546, 1.51677641228, 7.17475582739}
_____
In the folder "iteration for solutions" is an equation for Newton's method iteration, essentially, ...
g(x) = x -f(x)/f'(x)
where f(x) is defined as shown in the picture.
Many graphing calculators can compute a numerical derivative, so you can essentially write the formula in this form without having to do the derivative-taking yourself. This calculator is nicely interactive, so the iteration result is produced at the same time the argument for g(x) is entered. Essentially, you write the answer by copying the answer using the 4-digit zero-crossing values shown on the graph as the iteration starting point.