Nicole took out a 30-year mortgage for $90,000 at 7.5%. How much is her monthly mortgage payment? I assume $675,000?
1 answer:
Answer:
- Nicole pays $629.29 per month
- Zack pays $563.24 per month
Step-by-step explanation:
We're not quite sure why you estimated the monthly payment at several times the value of the entire loan.
The applicable formula is the amortization formula. It computes the monthly payment A on loan principal value P at annual rate r for t years to be ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
The value of r used in this formula is the decimal equivalent of the percentage rate. 7.5% = 0.075; 9% = 0.09
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<h3>a)</h3>The formula with Nicole's numbers filled in looks like ...
A = $90,000(0.075/12)/(1 -(1 +0.075/12)^(-12·30))
= $90,000(0.00625)/(1 -(1.00625^-360)) = $562.50/(1 -0.1051398)
A ≈ $629.293 ≈ $629.29 . . . . Nicole's monthly payment
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<h3>b)</h3>Using the same formula with P=$70,000, r=0.09, t=30, we find Zack's monthly payment to be $563.24.
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<em>Additional comment</em>
If you're doing a number of problems of this type, it can be helpful to use a tool that will do the calculation for you without error. A graphing calculator or spreadsheet can do that. One example is shown in the attachment.
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So if we graph this function we will get the Figure below. Thus, let's study both the equation and the graph to get some conclusions. Therefore, we can assure these statements:
First. The function is defined only for
as shown in the Figure. This is also true because of 
where 
must be greater (or equal) than zero.
Second. The range of the function are the values of
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Third. If creases then 
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First. The function is defined only for
Second. The range of the function are the values of
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Answer:
-3.98 (nearest hundredth)
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
Given interval: -2 ≤ x ≤ 2
Substituting the values into the equation: