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sergeinik [125]
3 years ago
11

Beverly Frost bought a home for $190,000 with a down payment of $19,000 at 7% for 25 years. Since then the rate has risen to 9%.

How much more would her monthly payment be if she bought the house at 9%?
Mathematics
1 answer:
Trava [24]3 years ago
3 0
We start by figuring out the present value of the remaining balance for the home, which is 190000 - 19000 = 171000.  We must also figure out the monthly interest rate, since the rate given does not say it is a nominal rate, nor does it say it is compounded monthly, so we assume that is is NOT a nominal rate.  Let's call them i7 and i9.  So i7 = (1.07^(1/12) - 1) = .00565415 and i9 = (1.09^(1/12) - 1) = .00720732.
Now we just have to figure out the monthly payment under both interest rates.  At 7%, we have 171000 = x * a angle 300
which becomes 171000 = x * (1 - 1.00565415^-300)/.00565415
So, the monthly payment, x7 is 1185.24.
At 9%, we have 171000 = x * a angle 300 (at the i9 rate)
which becomes 171000 = x * (1 - 1.00720732^-300)/.00720732
So, the monthly payment, x9 is 1394.13.
The difference between monthly payments would be 1394.13 - 1185.24 = 208.89, which is the final answer.
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<h3><u>Explanation</u></h3>
  • Meaning of f(a)

f(a) means the value of f(x) is ... when x = a. That means if we substitute x = 3, we would get f(3).

f(3) also means the value of f(x) is ... when x = 3.

f(x) can also be defined as y // f(x) = y

  • Find f(3) by graph.

You can find the value of f(x) at specific domain from the graph by looking at x = 3 then look up to where the point or where the graph passes. From the graph, when x = 3 as we look up and the graph passes y-coordinate at 1.

Therefore we can say that when x = 3, y = 1.

<h3><u>Answer</u></h3>

f(3) = 1

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Step-by-step explanation:

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How are rational functions similar to linear, quadratic, or exponential functions? How are they different? When are these simila
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Answer:

See explanation below for further details.

Step-by-step explanation:

A rational consist of two real numbers such that:

\frac{a}{b} =c

If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.

If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example:

If a = x^{2} and b = x, then:

c = \frac{x^{2}}{x}

c = x

If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example

If a = 3\cdot x^{3} and b = x, then:

c = \frac{3\cdot x^{3}}{x}

c = 3\cdot x^{2}

But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.

Example

If a = 10^{2x} and b = 3\cdot 10^x, then:

c = \frac{10^{2\cdot x}}{3\cdot 10^{x}}

c = \frac{1}{3}\cdot 10^{2\cdot x -x}

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Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.

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It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.

Example

5\cdot a^2\cdot x -9

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