Answer:
The mortgage chosen is option A;
15-year mortgage term with a 3% interest rate because it has the lowest total amount paid over the loan term of $270,470
Step-by-step explanation:
The details of the home purchase are;
The price of the home = $275,000
The mode of purchase of the home = Mortgage
The percentage of the loan amount payed as down payment = 20%
The amount used as down payment for the loan = $55,000
The principal of the mortgage borrowed, P = The price of the house - The down payment
∴ P = $275,000 - 20/100 × $275,000 = $275,000 - $55,000 = $220,000
The principal of the mortgage, P = $220,000
The formula for the total amount paid which is the cost of the loan is given as follows;
[tex]Outstanding \ Loan \ Balance = \dfrac{P \cdot \left[\left(1+\dfrac{r}{12} \right)^n - \left(1+\dfrac{r}{12} \right)^m \right] }{1 - \left(1+\dfrac{r}{12} \right)^n }[/tex]
The formula for monthly payment on a mortgage, 'M', is given as follows;
[tex]M = \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}[/tex]
A. When the mortgage term, t = 15-years,
The interest rate, r = 3%
The number of months over which the loan is payed, n = 12·t
∴ n = 12 months/year × 15 years = 180 months
n = 180 months
The monthly payment, 'M', is given as follows;
M =
The total amount paid over the loan term = Cost of the mortgage
Therefore, we have;
220,000*0.05/12*((1 + 0.05/12)^360/( (1 + 0.05/12)^(360) - 1)
[tex]M = \dfrac{220,000 \cdot \left(\dfrac{0.03}{12} \right) \cdot \left(1+\dfrac{0.03}{12} \right)^{180} }{\left(1+\dfrac{0.03}{12} \right)^{180} - 1} \approx 1,519.28[/tex]
The minimum monthly payment for the loan, M ≈ $1,519.28
The total amount paid over loan term, A = n × M
∴ A ≈ 180 × $1,519.28 = $273,470
The total amount paid over loan term, A ≈ $270,470
B. When t = 20 year and r = 6%, we have;
n = 12 × 20 = 240
[tex]\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.06}{12} \right) \cdot \left(1+\dfrac{0.06}{12} \right)^{240} }{\left(1+\dfrac{0.06}{12} \right)^{240} - 1} \approx 1,576.15[/tex]
The total amount paid over loan term, A = 240 × $1,576.15 ≈ $378.276
The monthly payment, M = $1,576.15
C. When t = 30 year and r = 5%, we have;
n = 12 × 30 = 360
[tex]\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.05}{12} \right) \cdot \left(1+\dfrac{0.05}{12} \right)^{360} }{\left(1+\dfrac{0.05}{12} \right)^{360} - 1} \approx 1,181.01[/tex]
The total amount paid over loan term, A = 360 × $1,181.01 ≈ $425,163
The monthly payment, M ≈ $1,181.01
The mortgage to be chosen is the mortgage with the least total amount paid over the loan term so as to reduce the liability
Therefore;
The mortgage chosen is option A which is a 15-year mortgage term with a 3% interest rate;
The total amount paid over the loan term = $270,470
Grade low in math help if you can :) Geometry
Lauren wants to build a model airplane using a scale where 2 inches represents 15 feet. If the airplane is 75 feet long, how long should the model be?
A.
5 inches
B.
7.5 inches
C.
10 inches
D.
15 inches
Answer:
C) 10 inches
Step-by-step explanation:
I think the simplest way to do this is as follows:
divide 75 by 15 to get how many times you need to multiply 2in by
75/15=5
since 15(5)=75 or the actual size of the airplane,
2(5)=10 which is the size of the model airplane
PLEASE HELP ASAP NO LINKS PLEASE A relationship between education and income is given in the table. Based on the data, how much more does a person with a bachelor's degree earn than a person with a high school diploma over the course of 15 years?
A)$387,075
B)$398,730
C)$753,585
D)$785,805
Degree of education Income
High school diploma $26,582
Associate's degree $37,955
Bachelor's degree $52,387
Master's degree $59,995
Doctoral degree $76,821
Nick used his credit card to make several large purchases, and now owes the credit card company $4,273 plus 32% interest. His mother gave him $500 for his birthday. Which is the most responsible choice he can make regarding his birthday money?
A.
He can use all the money to pay down his credit card debt.
B.
He can invest $200 in the stock market and pay down his credit card debt with the rest.
C.
He can put $250 into a savings account that pays 3.8% interest and pay down his credit card debt with the rest.
D.
He can put all the birthday money in the 3.8% savings account.
Answer:
Step-by-step explanation:
A, because more debt would build up for your credit card if you added money to a savings account since you would have to wait a whole year to get interest back. And it wouldn't be B because it simply would not be worth it to invest in stocks while in debt. Also, I just took the test and got it right!
HELPPPP FASTTTTTT no links or bad answers.
Answer:
The first answer is Surface Area and the second answer is Volume.
Step-by-step explanation:
Remember that Surface Area is the sum of ALL surfaces on a 3D shape. Volume is the amount of space of a three dimensional figure, which is measured in cubic units.
My Explanation:
The first one is surface area because the cube is a 3D shape and it is measured by 5in. The second one is volume because it has three dimensions: 15 inches by 12 inches by 3 inches and it is measured in cubic units.
I hope this answers your question! :)
Answer: Surface area, Volume
Step-by-step explanation:
If θ is an angle in standard position and its terminal side passes through the point (21,-20), find the exact value of \cot\thetacotθ in simplest radical form.
The exact value of the cotangent of theta in simplest radical form is -21/20.
What is the simplest radical form?
The simplest radical form is the expression of a radical without any factors inside the radical that can be further simplified.
To find the exact value of cotangent of theta, we need to find the values of cosine and sine of theta first.
Given that the terminal side of the angle passes through the point (21,-20), we can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the angle and the x and y-axes:
[tex]h = \sqrt{(21^2 + (-20)^2)} = \sqrt{(841 + 400)} = \sqrt{(1241)}[/tex]
Then, we can find the values of cosine and sine of theta using the x and y-coordinates of the point:
cos(theta) = adjacent/hypotenuse = 21/sqrt(1241)
sin(theta) = opposite/hypotenuse = -20/sqrt(1241)
Now we can find the value of cotangent of theta:
cot(theta) = cos(theta) / sin(theta) = (21/sqrt(1241)) / (-20/sqrt(1241))
= -21/20
Therefore, the exact value of the cotangent of theta in simplest radical form is -21/20.
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Kyle held a balloon 8ft off the ground above his head and Ava is standing 15 feet directly to g the right of Kyle how far is Ava from the balloon
Answer:
17
Step-by-step explanation:
Pythagorean theory baby! Okay so the Pythagorean theory is a² + b² = c² so lets draw a triangle and label our sides. So we know 8² + 15² = c² so I'm going to find the square root of all of our numbers. We get 64 + 225 = c² so then add 64 + 225 = 289 then I take the square root of 289 which equals 17 . This answer also makes sense because out hypotenuse should always be bigger then the legs.
I'm pretty sure thats right, Hope this helps.
Q 18: Melissa uses 150 g of sugar for every 6 eggs. How many eggs should she use with 350 g of
sugar?
Answer:
14 eggs
Step-by-step explanation:
150 grams need 6 eggs
1 gram need 6 ÷ 150 eggs
350 grams need 350×6÷ 150 = 14 eggs
Type the correct answer in each box. Use numerals instead of words.
Bethany collected 200 survey responses regarding recycling behaviors in her city of those responses, 174 people responded that they
participate in the city's recycling program.
Use this information to complete the statement. Round all answers to the nearest hundredth.
, which means that
% of the people surveyed do not participate in the city's
The approximate sample proportion is
recycling program.
Answer:
Step-by-step explanation:
Answer:
1st one 0.87
2nd one 13
PLATO
Step-by-step explanation:
an astronaut drops a rock off the edge of a cliff on the moon. the distance, d(t), in meters, the rock travels after t seconds can be modeled by the function d(t) = 0.8t^2. what is the average speed, in meters per second, of the rock between 5 & 10 seconds after it was dropped?
Answer:
The average speed between the times given is 12 m/s
Step-by-step explanation:
Here, we want to calculate rate of change between the times given
Mathematically , we can get the average rate of change using the formula
f(b)-f(a)/b-a
in this case, b = 10 s and a = 5 s
f(b) is d(10) = 0.8(10)^2 = 80
f(a) is d(5) = 0.8(5)^2 = 20
Rate of change is thus;
(80-20)/(10-5) = 60/5 = 12 m/s
convert five whole five over eight from fraction to decimals
Answer:
5.625 is the correct answer to convert five whole five over eight from fraction to decimals.
Step-by-step explanation:
=5/8+5
=0.625+5
=5.625#
8. A truck is carrying peach juice, pear juice,
and grape juice bottles in a ratio of 4:3:5. If
there are 76 peach juice bottles, then how many
pear juice bottles are there?
Answer:
57 pear juices
Step-by-step explanation:
because we know we have 76 peach juices and the ratio is 4, so we get 19. This means that 19=x. And then we multiply 19 by 3 and we get 57.
❗❗❗PLS I NEED HELP ON THIS I DON'T UNDERSTAND PLS HELP❗❗❗❗❗❗
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Help
Write an equation in slope-intercept form of the line that passes through the given points.
Answer:
y = 1/2x+1
Step-by-step explanation:
Slope = Δy/Δx
The difference is y increases by 1 and difference in x increases by 2. So the slope is 1/2.
Slope-intercept form: y=mx+b
We take point (0,1) and input into this equation.
1= 1/2×0 +b
1 = b
PLZZ HELP!!!! ASAP PLZ!!!!
XTRA POINTS!!!
Answer:
38.1 cm²
Step-by-step explanation:
area of full circle = π6² = 113.04 cm²
area of 150° segment = (150/360)(113.04) = 47.1 cm²
triangle base = sin 75° x 6 x 2 = 11.59
triangle height = cos 75° x 6 = 1.553
area of triangle = 1/2(11.59)(1.553) = 9 cm²
150° segment - triangle = 47.1 - 9 = 38.1 cm²
6. Samuel runs 100 yards in 16 seconds. Jake runs 150 yards in 30 seconds. Who had the greater
speed while running? Justify your answer.
Answer:
samuel runs 200 yards in 32 seconds, while jake runs 15o yards in 30 seconds. samuel has greater speed than jake
Step-by-step explanation:
plzzzzz help i really need it guys thxxxxxxxx!
Answer:
11. m=-1/4 b=5 equation is y=-1/4x+5
12.m=4/3 b=0 equation is y=4/3x
Step-by-step explanation:
Question 3 of 10
What is the formula for finding the break-even point?
A. Break even point =
(0.125)(# of points)
monthly savings
B. Break even point =
(0.01)(# of points) (P)
monthly savings
C. Break even point =
(0.125)(# of points) (P)
monthly savings
D. Break even point =
(0.01) (# of points)
monthly savings
SUB
Answer: B. Break even point=(0.01)(# of points)(P) / monthly savings
Step-by-step explanation: took the quiz.
The formula for finding the break-even point is: Break-even point = Fixed costs ÷ (Unit price - Variable costs per unit).
What is break-even point?The break-even point is the point at which a company's total revenue from sales equals its total costs, resulting in a profit of zero. There is no profit or loss at the break-even point.
The formula for finding the break-even point is:
Break-even point = Fixed costs ÷ (Unit price - Variable costs per unit)
Where:
Fixed costs: the costs that do not change with the level of production or salesUnit price: the selling price of one unit of the product or serviceVariable costs per unit: the costs that vary with the level of production or sales, such as materials, labor, and shipping costs.Thus, the break-even point is the point at which the total revenue from sales equals the total costs, so there is neither a profit nor a loss.
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Find the distance between the pair of points (6. - 22) and (1. - 23) The distance is
if y=27 when x= 8 find y when x =11
Answer:
37 1/8
Step-by-step explanation:
The problem probably assumes direct variation
y=kx
IF so, then plug in the values and solve for k
27=k(8)
k = 27/8
y= (27/8)x. Now let x = 11
y = (27/8)11 = 27(11)/8 = 37.125 = 37 1/8
y = 37 1/8
the problem is making some assumption about the relation between x and y. The simplest assumption that's likely is direct variation, that x and y are linearly related. The graph is a straight line through the origin with slope = 27/8
need help!!!!!!!!!!!!!!!!!!!
Answer:Table 3 i think
Step-by-step explanation:
PLS HELP IVE BEEN ASKING FOR 4 HOURS NOT A SINGLE PERSON HAS BEEN RIGHT ITS PAST DUE :( JUST TROLLS I WILL GIVE BRAINLIEST JUST PLS HELP
Answer:
square on the side - 7
first square on top 3
last square 10
Step-by-step explanation:
Darius makes a shirt for $8. He sells the shirt for $18. By what percentage did Darius increase the cost of the shirt?
Answer:
225%
Step-by-step explanation:
Please can someone help me out with this- I’m really stuck on this problem and I can’t get off of it cause I failed it to much :/
When you exercise, your target heart rate r at 70% can be determined by the formula r = 0.7(220 − a) where a represents your age in years. Solve the formula for a.
PLEASE HELP
If a triangle has sides with lengths of 10 inches 12 inches and 14 inches is a right triangle?
Answer:
not a right triangle
Step-by-step explanation:
right triangles are those that prove out to be true when you square the two smaller sides and the sum is equal to the square of the longest side
true or false?
10² + 12² = 14²
100 + 144 = 196
False, ∴ not a right triangle
find the arc length of the bolder arc
A) 283.5 mi
C) 733.0 mi
B) 10.2 mi
D) 73.3 mi
Answer:
d its d :)
Step-by-step explanation:
i already did that
Profit, P(x), is the difference between revenue, R(x), and cost, C(x), so P(x) = R(x) - C(x). Which expression represents P(x), if R(x) = 2x^4 – 3x^3 + 2x – 1 and C(x) = x^4 – x^2 + 2x + 3?
Answer:
x^4-3x^3+x^2-4
Step-by-step explanation:
Given the following functions
R(x) = 2x^4 – 3x^3 + 2x – 1 and
C(x) = x^4 – x^2 + 2x + 3
We are to find the profit function P(x)
P(x) = R(x) - C(x)
P(x) = 2x^4 – 3x^3 + 2x – 1 - ( x^4 – x^2 + 2x + 3)
P(x) = 2x^4 – 3x^3 + 2x – 1 - x^4 + x^2 - 2x - 3
Collect the like terms
P(x) = 2x^4-x^4-3x^3+x^2+2x-2x-1-3
P(x) = x^4-3x^3+x^2+0-4
P(x) = x^4-3x^3+x^2-4
Hence the required profit function P(x) is x^4-3x^3+x^2-4
Answer:
x^4-3x^3+x^2-4
Step-by-step explanation:
Suppose that the path of a newly discovered comet could be modeled by using one branch of the equation x2/4 - y2/9=1, where distances are measured in astronomical units. Name the vertices of the hyperbola and then graph the hyperbola.
Answer:
the answer is A just tool the quiz lesson 5 hyperbolas Algebra 2B unit 5 these are the correct answers
1.A
2.B
3.D
4.A
5.B
6.D
7.A
hopes this helps everyone
The hyperbola has two vertices at (-2,0) and (2,0)
We have given that the equation
[tex]\frac{x^2}{4}-\frac{y^2}{9}=1[/tex]
What is the equation of the hyperbola?[tex]\frac{x^{2} }{a^2}+\frac{y^2}{b^2} =1[/tex]
Compare the above equation of the hyperbola with given equation
therefore a=2
vertices are (-a,0) and (a,0)
Therefore the vertices are (-2,0) and (2,0)
See the graph of the hyperbola in link given below.
The hyperbola has two vertices at (-2,0) and (2,0)
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The 819 runners in a race are divided into 6 different groups as equally as possible. How many extra runners are in the last group
Answer:
3 runners will be in the last group
Step-by-step explanation:
So first you need to divide the 819 runners into 6 different groups. Once you do this... you get a total of 136. So there are 136 runners in each of the 6 groups. However, once you get to the end of the division problem, there is a remainder of 3. These three stand for the last 3 runners. Giving you your answer.
I hope this helps you!!!
I'll give you a brainiest, but please help me with this question. I need help.
Hope it helps you!.......
Answer:
Angle B would be 56 degrees.