a first time homebuyer is given the choice of two loans: loan a: 390,000, 15 year-fixed, 4 discount points, M=$3,509.71. loan b: 390,000, 15 year-fixed, 0 discount points, M=3,659.86. how much does the hole buyer save in total by choosing loan A? a) 27,027 b) 11,427 c) 26,351.02 d) 42,627.05

A First Time Homebuyer Is Given The Choice Of Two Loans: Loan A: 390,000, 15 Year-fixed, 4 Discount Points,

Answers

Answer 1

If a first time homebuyer is given the choice of two loans: loan a: 390,000, 15 year-fixed, 4 discount points. The amount the hole buyer save in total by choosing loan is:  b) 11,427.

How to find the saved amount?

To compare the total cost of each loan, we need to calculate the total payments made over the life of the loan.

For loan A, the monthly payment is $3,509.71 and the loan term is 15 years, so the total payments would be:

Total payments = monthly payment x number of months

Total payments = $3,509.71 x (15 x 12)

Total payments = $631 747.8

However, loan A also has a 4-point discount, which means the borrower paid 4% of the loan amount upfront to reduce the interest rate.

Discount points = loan amount x discount rate

Discount points = $390,000 x 0.04

Discount points = $15,600

To calculate the total cost of loan A, we need to add the discount points to the total payments:

Total cost of loan A = total payments + discount points

Total cost of loan A = $631 747.80 + $15,600

Total cost of loan A = $647,347.80

For loan B, the monthly payment is $3,659.86 and the loan term is 15 years, so the total payments would be:

Total payments = monthly payment x number of months

Total payments = $3,659.86 x (15 x 12)

Total payments = $658,774.5

To calculate the total cost of loan B, we simply add the total payments:

Total cost of loan B = total payments

Total cost of loan B =  $658,774.5

Therefore, the total amount saved by choosing loan A over loan B is:

Savings = total cost of loan B - total cost of loan A

Savings = $658,774.5 - $647,347.80

Savings = $11,427

Therefore, the answer is option b) $11,427.

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Related Questions

Emily parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded annually. What will be the total balance after 2 years?
Responses

$3,273.50
$3,273.50

$1,757.71
$1,757.71

$2,385.72
$2,385.72

$1,314.08

Answers

Answer:

B

Step-by-step explanation:

Using the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = final amount

P = principal (starting amount)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = time (in years)

We can plug in the given values:

P = $1,500

r = 0.0825 (8.25% expressed as a decimal)

n = 1 (compounded annually)

t = 2

A = $1,500(1 + 0.0825/1)^(1*2)

A = $1,500(1.0825)^2

A = $1,757.71

Therefore, the total balance after 2 years will be $1,757.71. Answer choice B is correct.

Ted jogged a total of 11.2 miles in 4 days. He jogged the same distance each day.

Part A
How far did he jog each day? Enter your answer in the box.

2.8
miles

Part B
How many total miles would Ted jog if he continued to jog the same number of miles each day for 6 days? Enter your answer in the box.

miles? put answer bellow for part b

Answers

Answer: 16.8 miles

Step-by-step explanation:

Multiply 2.8 miles by 6 to find the number of miles jogged after 6 days.

Answer:

16.8 miles!

Step-by-step explanation:

Help!!! I need help I don't know how to do it

Answers

100% of 42 people=42
50% of 42 people =21
150% of 42 people=63

Hope it helps : )

What is the linear equation represented by the graph?

Answers

The linear equation represented by the graph is y = 8x.

Describe Linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional space. It can be written in the form of:

y = mx + b

where y and x are variables, m is the slope of the line, and b is the y-intercept of the line (the point where the line crosses the y-axis).

The slope, represented by "m", describes the steepness of the line, while the y-intercept, represented by "b", is the point where the line intersects with the y-axis.

Linear equations can also be written in other forms, such as the standard form:

Ax + By = C

where A, B, and C are constants, and x and y are variables. In this form, the equation describes a line in terms of its x and y intercepts.

Linear equations are used in a variety of fields, including mathematics, physics, engineering, economics, and more. They are useful for describing and predicting relationships between variables that exhibit a linear pattern.

The equation represented by the graph is a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

m = (y2 - y1)/(x2 - x1)

Let's choose the first two points (0.5, 4) and (1, 8):

m = (8 - 4)/(1 - 0.5) = 8

So, the slope is 8.

To find the y-intercept, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Let's choose the point (0.5, 4) and the slope we just found:

y - 4 = 8(x - 0.5)

y - 4 = 8x - 4

y = 8x

So, the linear equation represented by the graph is y = 8x.

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Pls help 23736 x 2858=?

Answers

Answer:

23736 x 2858

= 67837488

Step-by-step explanation:

You're welcome.

Answer:

67837488

Step-by-step explanation:

24 X 3 X 23 X 43 X 1429

How do you calculate the arc length of a circle?

Answers

To calculate the arc length of a circle, you need to use the formula: arc length = (central angle in radians) x (radius)

where the central angle is measured in radians and the radius is the distance from the center of the circle to the edge. To use this formula, first convert the central angle from degrees to radians by multiplying it by π/180. Then, multiply the result by the radius to find the arc length. For example, if you have a circle with a radius of 5 units and a central angle of 45 degrees, you can calculate the arc length as follows: Convert the central angle to radians: 45 x π/180 = 0.7854 radians. Multiply the central angle in radians by the radius: 0.7854 x 5 = 3.927 unit. Therefore, the arc length of a circle with a radius of 5 units and a central angle of 45 degrees is 3.927 units.

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in the xy-plane, the lines y=3x-5 and y=-2x+10 intersect at a point (h,k). what is the value of k?

Answers

Answer:

(3,4)

k is 4

Step-by-step explanation:

See attached graph.

f(x) = − ³/2 x and g(x) = (½)² – 1
-
Graph the functions on the same coordinate plane.
Let
What are the solutions to the equation
?
f(x) = g(x) ₂

Answers

The solution to the equations have the coordinates of (-6.61, 9.91) and (0.61, -0.91)

How to determine the solution to the system of equation

From the question, we have the following parameters that can be used in our computation:

f(x) = − ³/2 x and g(x) = (½)² – 1

Express the equation properly

So, we have

f(x) = -3/2x

g(x) = (1/2x)^2 - 1

Next, we make a plot of the system to determine the solution

The point of intersection in the plot represent the solution to the equations

In this case, the point of intersection has a coordinate of (-6.61, 9.91) and (0.61, -0.91)

Hence, the solution is (-6.61, 9.91) and (0.61, -0.91)

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Use the circle graph shown below to answer the question.

If 30 sixth graders own birds, how many sixth graders were surveyed?

Answers

The total number of sixth graders surveyed is 600 sixth graders

Solving statistics problem using pie charts

The given diagram is a pie chart with different percent of pet owned by sixth graders.

We need to determine the number of sixth grader surveyed if 30 sixth graders own birds.

Number of birds = 5% of the total sixth graders

Substitute the given parameters

30 = 0.05 * T

T = 30/0.05

T = 600

Hence is 30 sixth graders own birds, then 600 sixth graders were surveyed.

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Give three solutions to the equation y=1/2x+1

Answers

Answers:

(12, 7)

(20, 11)

(32, 17)

There are infinitely many possible answers.

=======================================================

Explanation:

The equation given to us is the same as y = 0.5x+1 because 1/2 = 0.5

If we replace x with even numbers, then we'll get whole number outputs for y.

Example: if x = 12, then y = 0.5x+1 = 0.5*12+1 = 7

This leads to (12,7) as one solution to this equation. A solution is a point that is on the line. Use graphing software like Desmos or GeoGebra to confirm.

Another example: if x = 20, then y  = 0.5x+1 = 0.5*20+1 = 11. Therefore, another solution point is (20, 11)

Final example: If x = 32, then y = 0.5x+1 = 0.5*32+1 = 17. This gives the point (32,17)

There are infinitely many possible answers since we can replace x with infinitely many real numbers.

How do I solve this?

Answers

The given triangles are similar by SSS theorem

Similarity property of a triangle

The given figures are similar triangles with 3 sides and angles. There are several ways triangles can be proved to be similar such as the AAS, SSS, SAS etc theorems.

For the given triangles, if the ratio of their similar sides is equivalent  to the same constant, then the triangles are similar.

AC/HF = AB/HG = CB/GF = k

84/14 = 72/12 = 48/8

84/14 = 6

72/12 = 6

48/8 = 6

Since the ratios are all equal, hence the triangles are similar

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the longer diagonal of a field in the shape of a quadrilateral is 120 m and the length of the perpendiculars from the opposite vertex upon a longer diagonal is 20 m and 30 m find the area of the field Step by Step Explaination class 8 lesson no 11 mensuration

Answers

The area of the field is 900√10 m².

What is the Pythagorean theorem?

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Quadrilateral ABCD.

The longer diagonal connects vertices A and C, and let E and F be the feet of the perpendiculars from vertices B and D to the longer diagonal AC.

From the figure,

BE = 20 m

DF = 30 m

AE = EC = 120/2 = 60 m

Now,

The area of the quadrilateral.

The area of a trapezoid.

= (sum of parallel sides) x (height) / 2

Using the Pythagorean theorem,

AB² = AE² + BE²

60² + 20² = 4000

AB = √(4000)

AB = 20 √10

And,

CD² = CE² + DF²

CD² = 60² + 30²

CD² = 4500

CD = √(4500)

CD = 15 √20

Now,

Area = AB + CD x 1/2 x AC

= 20√10 + 15√20 x 1/2 x 120

= 900√10

Therefore,

The area of the field is 900√10 m².

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The cost of putting on a play is $500 for the theater rental, $500 for the actors, and $750 for set decorations and costumes. If tickets are sold for $25 each, how many tickets need to be sold to reach the break-even point?

Answers

Answer:

The total cost of putting on the play is $500 for theater rental + $500 for actors + $750 for set decorations and costumes = $1750.

To reach the break-even point, the revenue from ticket sales needs to equal the total cost, so $1750 = $25 x (number of tickets sold).

Solving for the number of tickets sold, we can divide both sides by $25: $1750 / $25 = (number of tickets sold).

This gives us: 70 = number of tickets sold.

Therefore, Mr. Curry needs to sell 70 tickets to reach the break-even point.

Step-by-step explanation:

What is the definition of covariance

Answers

Answer:

indicates the relationship of two variables whenever one variable changes.

Step-by-step explanation:

Urgent! Can you help me solve these 3 numbers with detailed steps please!

Answers

d)  whenther there the limit is going to infinity like that

take the large term on the top and the largest one on the bottom

so;

4x^5/12x^2 =

basically if you continued to plug it in it would give you

4x^5/12x^2

eventually 12x^2 would = 24 because you would get 12x^2 to 24x^1, take the dervative = 24

for the top it would go from 4x^5; 20x^4; 80x^3

then you would have 80x^3/24

plug in infinity for x

infinity/24

Find the range, IQR, and MAD of the data set.
15, 22, 16, 13, 14, 20, 40, 44

Answers

IQR =  16.5

The range = 31

Mean absolute deviation = 9.5

What is the median?

The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.

Given:

A data set:

15, 22, 16, 13, 14, 20, 40, 44.

The lower half of median Q1 = (14 + 15)/2 = 14.5

The upper half of median Q3 = (40 + 22)/2 = 31

So IQR = Q3 - Q1 = 31 - 14.5 = 16.5

The range = 44 - 13 = 31

Mean absolute deviation = 9.5

Therefore, MAD = 9.5.

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Jayden measured a desk to be 4 feet. The actual measurement is 3.2 feet. What is Jayden's percent error?

Answers

The percentage error made by the person is 25%.

What is percentage error?

To get the percentage error, multiply the relative error by 100%. In other words, first, calculate the difference between the true value and the measured value. Then, divide the obtained difference by the true value. Then take the absolute value of the obtained result and multiply it by 100%.

The measured value is 4 feet.

The true value is 3.2 feet.

So, the difference between the true value and the measured value is (4 feet - 3.2 feet), that is, 0.8 feet.

Now, divide the obtained difference by the true value.

(0.8 feet)/(3.2 feet) = 1/4

= 0.25

To get the percentage error, take the absolute value of the obtained result and multiply it by 100%.

|0.25|×100% = 0.25×100%

= 25%

Therefore, the obtained answer is 25%.

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Solve for x and y

5x + y = 9
10x -7y = -18

Answers

Answer:

x=1; y=4

Step-by-step explanation:

for this system, you could use either substitution or elimination

i'll solve it both ways

SUBSTITUTION:

5x+y=9 becomes y=-5x+9

10x-7y=-18; substitue y from y=-5x+9

10x-7(-5x+9)=-18

10x+35x-63=-18

45x=45

x=1

substitue x into y=-5x+9

y=-5(1)+9

y=4

ELIMINATION

5x+y=9

10x-7y=-18

multiple the top equation by 7 to get 35x+7y=63

now, 7y and -7y cancel out

add the two equations to get 45x=45

x=1

substitute into 5x+y=9

5(1)+y=9

y=4

What is 10 percent of 20000?

Answers

To find 10 percent of 20000, you can multiply 20000 by 0.1, which gives you the answer of 2000.

0.1 × 20000 = 2000.

Here's the explanation of the calculation: When we want to find a certain percentage of a number, we can convert the percentage into a decimal by dividing it by 100. In this case, 10% is equivalent to 10/100, which simplifies to 0.1. Then, we can multiply 20000 by 0.1 to find the answer, which is 2000. In summary, to find 10% of a number, we can convert the percentage into a decimal by dividing it by 100, and then multiply the decimal by the original number.

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arge telescopes often have small fields of view. For example, the Hubble Space Telescope’s (HST’s) advanced camera has a field of view that is roughly square and about 0.06 degree on a side.
Calculate the angular area of the HST’s field of view in square degrees.
A. 0.006 Square degrees
B. 0.36 Square degrees
C. 0.0036 Square degrees
D. 0.06 Square degrees

Answers

The correct response is C. 0.0036 Square degrees The field of vision of the Hubble Space Telescope is only 0.006 degrees, which is around 100 times less than that of the Micro Observatory telescopes. But it has a 100 times better angular resolution!

Skywatchers can readily view planets with just a modest or medium-sized telescope. How much of our solar system is visible will wow you! Additionally, you don't need a completely dark sky to see all of the planets in our solar system; a telescope can still make Venus, Mars, Jupiter, and Saturn easily visible even when viewed in a city. From $100 to well over $10,000, a telescope can be purchased. In 2022, you can anticipate that a good telescope for visual observing will start around $300 and a telescope capable of deep-sky astrophotography would start around $800. With a 25x telescope, even the tiniest telescope should be able to see Saturn's rings.

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Large telescopes often have small fields of view. For example, the Hubble Space Telescope's (HST's) advanced camera has a field of view that is roughly square and about 0.06 degree on a side. Calculate the angular area of the HST's field of view in square degrees.

A. 0.006 Square degrees

B. 0.36 Square degrees

C. 0.0036 Square degrees

D. 0.06 Square degrees

3.In an online quiz, positive points are awarded for a correct answer, and negative
points are awarded for an incorrect answer. Elena answers 10 questions correctly and
4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.

a. Write a system of equations that describes Elena's and Kiran's scores. Usex to
represent the number of points for a correct answer and y to represent the
number of points for an incorrect answer.
that


X represents number of points and y represents incorrect answer

Answers

The system of equations can be written as:-

10x + 4y = 42

6x + 8y = 14

What is a system of equations?

A system of equations, also known as a set of simultaneous equations or an equation system, is a finite set of equations for which we sought common solutions in mathematics. A system of equations can be classified in the same way that a single equation can.

Given that in an online quiz, positive points are awarded for a correct answer, and negative points are awarded for an incorrect answer. Elena answers 10 questions correctly and 4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.

The system of equations can be written as:-

10x + 4y = 42

6x + 8y = 14

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Helppp

A circle has an arc whose measure is 80 degrees and whose length is 88pi. What is the diameter of the circle?

Answers

The diameter of the circle is 396 units

What is a diameter?

The diameter is the length of the line through the center that touches two points on the edge of the circle.

A diameter is twice the radius of a circle.All diameters are segment but not all segments are diameter.

length of an arc = tetha/360 × πd

l = 80/360 × π d

88π = 80/360 × π d

80d = 88× 360

80d = 31680

divide both sides by 80

d = 31680/ 80

d = 396 units

therefore the diameter of the circle is 396 units

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An air navigation system spots two planes converging to a point at right angles and at colliding speeds. The planes are flying at 560 mph and 900 mph and are at 280 miles and 450 miles from the point, respectively. At what rate, in mph, is the distance between the planes decreasing?

Answers

The distance is decreasing at a rate of 1028.30 miles/hour.

What is Rate of Change?

An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.

Plane X: The first plane is due west of you, or at x = -280

traveling towards you at 560 mph

Plane Y: The second plane is due south of you, or at y = -450

traveling towards you at 900 mph.

D = Distance between the two planes.

D = √( x² + y² )

d/dt [ D ] = d/dt [ √( x² + y² ) ]

dD/dt = 1 / 2√( x² + y² ) (2XX' + 2YY')

dD/ dt = 1/2 √(-280)² + (-450)² (2 (-280)(560) + 2(-450)(900)

dD/ dt = 1/2 √(-280)² + (-450)² (2 (-280)(560) + 2(-450)(900))

dD/ dt = 1/ 530 (-140,000 - 405, 000)

dD/ dt = -1028.30

Thus, The distance is decreasing at a rate of 500 miles/hour  

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The sum of deviations of the individual observations from their sample mean isO sometimes greater than and sometimes less than zero, depending on the observations O always less than zero O always greater than zero O We do not have enough info to answer this questionO always equal to zero

Answers

The sum of deviations of the individual observations from their sample mean is always equal to zero.

The sum of deviations of the individual observations from their sample mean is always equal to zero. This is because the sum of all the deviations is the sum of a positive and a negative value. When we add the negative value to the positive value, the net result is always zero.To illustrate this, let's take an example. Suppose we have a sample of 5 observations: 2, 4, 6, 8, 10. The mean of the sample is 6. The deviations of the individual observations from the sample mean can be calculated as follows:

2-6=-4

4-6=-2

6-6= 0

8-6= 2

10-6=4

When we add the deviations, we get: -4+(-2)+0+2+4=0. The sum of all the deviations is always equal to zero.

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whats is 5.2r-2.4=8.7

Answers

The value of r is 2.134

in the equation, we would first

add 2.4

to both sides:

5.2r - 2.4 + 2.4 = 8.7+ 2.4

5.2r = 11.1

now we will

divide both sides by 5.2

to isolate the variable "r"

[tex]\frac{5.2r}{5.2} = \frac{11.1}{5.2}[/tex]

1r = 2.13461538

thus, the value of r = 2.134 approximately

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Suppose the cumulative distribution function of the random variable X is F(x) = 0 when x<-2 , F(x) = .25x + .5 when -2 <= x < 2 and F(x) = 1 when 2<=x (<= means greater than or equal). Determine the following a. P(X<1.8) b. P(X>-1.5) c. P(X<-2) d. P(-1

Answers

the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0.

a. P(X<1.8) = .25(1.8) + .5 = .95

b. P(X>-1.5) = .25(-1.5) + .5 = .375

c. P(X<-2) = 0

d. P(-1.5<X<2) = .25(2) + .5 - (.25(-1.5) + .5) = .875

a. For the probability P(X<1.8), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in 1.8 for x in the function to get F(1.8) = 0.25(1.8) + 0.5 = 0.95. Therefore, P(X<1.8) = 0.95.

b. For the probability P(X>-1.5), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375. Therefore, P(X>-1.5) = 0.375.

c. For the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0. Therefore, P(X<-2) = 0.

d. For the probability P(-1.5<X<2), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 and 2 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375 and F(2) = 0.25(2) + 0.5 = 0.95. Therefore, P(-1.5<X<2) = 0.95 - 0.375 = 0.875.

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PLEASE HELPPP
WILL GIVE BRAINLIEST!!!!!!

Answers

Julie is correct. If n=0 then you would get the fraction [tex]\frac{0}{0}[/tex] which is indeterminant (or undefined) since a zero is present in the denominator.

Marcy has 20$ she wants to buy a book that is marked down 30% from its original price of 28$ if the sales tax is 2.5% does marcy have enough money to buy the book

Answers

Answer:

yes

Step-by-step explanation:

if i did the math right marcy should have enough

A company is designing a new cylindrical package. The volume of the package is 87.92 in.3. The radius is 2 inches. Use the formula V = Bh and 3.14 to approximate π
to answer the questions.

Part A

To the nearest inch, how many inches is the height of the cylindrical package?


Part B

The company decides to keep the radius the same and double the height. Rounded to the nearest hundredth, how many cubic inches is the new volume of the package?

Answers

The height of the cylindrical package is 6 inches.

The new volume of the package is 88.26 cubic inches.

What is a cylinder?

A cylinder is a 3-D figure that has a radius and a height.

The volume of a cylinder is given as πr²h.

Example:

The volume of a cup with a height of 5 cm and a radius of 2 cm is

Volume.

= 3.14 x 2 x 2 x 5

= 62.8 cm³

We have,

Part A:

The formula for the volume of a cylinder is V = Bh, where B is the area of the base of the cylinder and h is its height.

For a cylinder with radius r and height h, the base area B is given by

B = πr².

Substituting the given values, we have:

V = Bh

87.92 = π(2²)h

h = 87.92 / (4π)

h ≈ 5.57

Rounding to the nearest inch, the height of the cylindrical package is 6 inches.

Part B:

If the company doubles the height of the cylinder while keeping the radius the same, the new height will be 2h = 2(5.57) = 11.14 inches.

The new volume can be calculated using the same formula:

V = Bh

V = π(2²)(11.14)

V ≈ 88.26 cubic inches

Rounding to the nearest hundredth, the new volume of the package is 88.26 cubic inches.

Thus,

The height of the cylindrical package is 6 inches.

The new volume of the package is 88.26 cubic inches.

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What does alpha 0.05 mean in stats?

Answers

An alpha value of 0.05 means that there is a 5% chance of incorrectly rejecting the null hypothesis.

In statistics, "alpha" is used to represent the significance level in a hypothesis test. The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is actually true.

In other words, if the p-value in a hypothesis test is less than or equal to 0.05, we can reject the null hypothesis and conclude that there is a statistically significant difference between the groups or variables being tested.

An alpha value of 0.05 is commonly used in research studies, but other values such as 0.01 or 0.10 may also be used depending on the desired level of significance.

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