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
Volume? serious answers please.
A gaming
console costs
$300 and has
8% tax. How
much is the tax?
$30 or $24?
Answer:
24
Step-by-step explanation:
8 percent of 300 is 24.
that should be right
Answer:
$24
Step-by-step explanation:
The tax is how much more you have to pay based on a percentage of the initial cost. The tax percent in this case is 8%. Since the console costs $300, we take 8% of $300 and charge it as the tax.
$300 * 8% = $300 * 0.08 = $24
If done by hand, move the decimal place on 0.08 to the left 2 times
0.08
00.8
008
This will give you 8. Multiply 8 by $300 which will give you $2400, next move the decimal to the right 2 times.
$2400.
$240.0
$24.00
Now you have $24
find value of X in cos(3x-30°)=sin(7x+50°)
Answer:
7
Step-by-step explanation:
Given the expression
cos(3x-30°)=sin(7x+50°)
In trigonometry cosx = sin(90-x)
Hence
Cos(3x-30) = sin(90-(3x-30))
Cos (3x-30) = sin(90-3x+30)
Cos (3x-30) = sin(120-3x)
Substitute into the expression above
Sin(120-3x) = sin(7x+50)
120-3x = 7x+50
Collect like terms
-3x-7x = 50-120
-10x = -70.
x = 70/10
x = 7
Hence the value of x is 7
Which set of sides would make a right angle?
8,10,12
4,5,6
5,12,13
5,10,12
Answer:
c
Step-by-step explanation:
Simplify the expression
[tex]5( \frac{1}{5} x - 1)(5x - \frac{1}{5} )[/tex]
Can someone help me with this problem?
Answer:
a) 2
b) 3
c) 1
hope this helps :)
The Buffalo football team Lost 12 yards then gained 27 yard during the next play what was the change in position
On wednesday 72% of the customers who bought gas at a gas station mad additional purchases. There were 250 customers who bought gas. how many of these 250 customers made additional purchases?
A=4 b=3 and c=2 work out 2b-3ac
Answer:
-18
Step-by-step explanation:
2b-3ac
2(3)-3(4×2)
6-3(8)
6-24
-18
Mica stands 75 feet away from the base of a tree and looks up towards the top of the tree at a 51 degree angle.
Answer:
Height of the tree = 92.61 feet
Step-by-step explanation:
Given: Distance between base of tree and Mica = 75 feet
Angle of elevation to the top of tree = 51°
Assuming we have to find the height of the tree = H
This can be found by applying simple trigonometry.
The height of the tree becomes perpendicular and distance between base of tree and Mica is base.
Then, tan51° = H/75
⇒ H = 75× tan51° = 92.61 feet
anyone know this?????
Answer:
(- 2, 1 ) and (1, 4 )
Step-by-step explanation:
Given the 2 equations
y = - x² + 5 → (1)
- x + y = 3 → (2)
Rearrange (2) expressing y in terms of x by adding x to both sides
y = x + 3 → (3)
Substitute y = x + 3 into (1)
x + 3 = - x² + 5 ( subtract - x² + 5 from both sides )
x² + x - 2 = 0 ← in standard form
(x + 2)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 1 = 0 ⇒ x = 1
Substitute these values into (3) for corresponding values of y
x = - 2 : y = - 2 + 3 = 1 ⇒ (- 2, 1 )
x = 1 : y = 1 + 3 = 4 ⇒ (1, 4 )
Step-by-step explanation:
its a false equasion x € R
Question 3
Translations, rotations, and reflections are rigid transformations that preserve side lengths and angle measurements. Find and record a series of
rigid transformations that will map the copied triangle to your original triangle. In the table, note the angles of rotation, lines of reflection, and
distances moved.
Answer:
Step
1 | Translate △DEF 7 units up.
2 | Translate △DEF 6 units to the left.
This is word by word so you may want to change it up a bit. Have a great day.
Step-by-step explanation: On PLATO, you may provide and record fewer steps. The answer will vary but may resemble an answer based off the mapping of △DEF to △ABC.
Answer:
Step-by-step explanation:
Find the mean of the following numbers:
32, 45, 33, 32, 43, 36, 38, 41, 39, 30, 44
Answer:
Step-by-step explanation:
Mean: 41+39+48+52+41+48+36+41+37+35/10
=41.8
Mode:41
Median:41
convert 32 grams to kilometer
Answer:0.032
Step-by-step explanation:
Pls HELPPPP HURRYYY PLSS
Answer:
A. 1 unit
Step-by-step explanation:
A cube has the same dimensions on each side, and the unit is 1 unit cube, none of the other options match.
You can easily rule out, B & D. That leaves you with A & C, and A makes the most sense, since 1 cubic unit would be the volume, and this question is only asking for the side length.
Good luck, hopefully, this helped!
A farmer planted corn in a square field. One side of the field measures 39 yards. What is the area of the cornfield?
Answer:
The area of the cornfield is 1,529 yards.
Step-by-step explanation:
In this case, since the statement indicates that it is a square field, you have to use the formula to calculate the area of a square, which is:
A=a², where:
A is the area
a is the lenght of side
The statement says that one side measures 39 yards, so this would be a, and you can replace this value on the formula:
A=39²
A=1,521
According to this, the answer is that the area of the cornfield is 1,529 yards.
2x + 10 =28
What is the solution to this equation?
Sammy made her uncle a garden. The width is 6 5 7 ft and the length is 7 3 5 ft. What is the area of the garden?
Answer:
482895ft^2
Step-by-step explanation:
Given data
Width= 657ft
Length= 735ft
We know that area A
A= Length* Width
A=657*735
A= 482895ft^2
Hence the area is 482895ft^2
first part to last question
Answer:
For question 4 you would have 1560000. For question 5 you would have 660000
Step-by-step explanation:
Find the area of the shaded figure
Answer:
its 56 units square.
Step-by-step explanation:
(count the tiles in the shaded figure, you'll get the area)
Describe the correlation between the amount spent and the number of people spending the money.
A. Negative correlation; as the amount spent increases, the number of people spendings that amount decreases
B. Negative correlation; as the amount spent increases, the number of people spending that amount increases
C. Positive correlation; as the amount spent increases, the number of people spending that amount decreases
D: Positive correlation; as the amount of spent decreases, the number of people spending that amount increases
Answer:
A. Negative correlation; as the amount spent increases, the number of people spendings that amount decreases.
It is so clear, just look at the graph and you will see exactly what im talking about
I NEED HELP ON THIS GEOMETRY QUESTION!!!
Answer:
c
Step-by-step explanation:
Hep plsssssssss it due at 12
Answer:
14: slope is 20
15: 5
Step-by-step explanation:
Solve my problem, PLEASE!!!!
Answer:
y=-3+15
Step-by-step explanation:
What is the equation of the graphed line written in
standard form?
2x + 3y = -6
2x + 3y = 6
y= -2/3x - 2
v= 2/3x - 2
Answer:
A. 2x + 3y = -6
Step-by-step explanation:
[tex](-3,0) (0,-2)[/tex]
[tex]slope:\frac{-2-0}{0+3} =\frac{-2}{3}[/tex]
[tex]y-0=\frac{-2}{3} (x+3)[/tex]
[tex]3y=-2x-6[/tex]
[tex]3y+2x+6=0[/tex]
[tex]2x+3y=-6[/tex]
-------------------
hope it helps...
have a great day!!
write the coefficient of h in 3d+h
really confused about this
Answer:
.22/63
Step-by-step explanation:
area = pi x R^2
A=22/7 * 1/3^2
Part I
compare the difference of the means of the two data sets found in part H as multiple m of their variability
Answer:
Step-by-step explanation:
I know that the two means are are 11.28 and 12.
I could be wrong but I did the math 5 times.
Answer:
the other guy is correct
Step-by-step explanation:
NEED HELP ASAP! DUE IN 3 MINUTES!!!
an electrician charges a $25 fee for a repair plus $15 per hour. Write an equation to model the total cost Y of a repair that takes X hours
22 and 21 please help no links or i report
Answer:
21) B. (5,45)
22) B. As the temperature decreases, hot chocolate sales increase.