The probability of drawing a vowel, replacing it, and then drawing a Z is 5/676.
The alphabet consists of 26 letters, and 5 of them are vowels (A, E, I, O, U). Hence, 5/26 of the time, a vowel will be drawn in the initial draw.
The likelihood of drawing a Z on the second draw is also 1/26, due to the fact that the card is changed after the first draw.
We can multiply the probabilities to determine the likelihood that both of these occurrences will occur:
P(Draw a Z after a vowel is drawn) = P(Draw a vowel) P(Draw a Z after the vowel is replaced) = (5/26) (1/26) = 5/676
As a result, the likelihood of drawing a Z after substituting a vowel is 5/676.
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Use the model below to calculate 2/3 x 3/4
A shop employs one man and one woman as shop assistants. The man works for 10 hours per day and the woman for 8 hours per day, and their wages per hour are in the ratio 7: 5. If the woman receives $24 per day, find the man's daily wage.
The man's daily wage is given as follows:
$42.
How to obtain the man's daily wage?The man's daily wage is obtained applying the proportions in the context of the problem.
The woman receives $24 for 8 hours of work, hence her hourly wage is given as follows:
24/8 = $3 per hour.
Their wages per hour are in the ratio 7:5, hence the man's hourly wage is obtained multiplying the woman's hourly wage by 7/5, hence:
7/5 x 3 = 21/5 = $4.2 per hour.
The man works 10 hours a day, hence the daily wage is given as follows, multiplying the hourly wage by 10:
10 x 4.2 = $42.
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The man's daily wage is $42.
How to find the man daily wage?We know that the woman works 8 hours per day and gets $24 per day, then her hourly pay is the quotient between these two values.
$24/8 = $3 per hour.
And we also know that their wages per hour are in the ratio 7: 5.
Then the man's hourly pay 7/5 times the hourly pay of the woman, then we just need to solve the product below:
(7/5)*$3 = x
(7/5)*$3 = $4.2
And the man works for 10 hours, then the daily wage is 10*$4.2 = $42.
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students were asked to choose their favorite subject if 2/9 of the students chose history and 3/9 chose biology what fraction chose either history or biology
Answer:
Step-by-step explanation:
To relate the angular motion of the hour hand (h) and the angular motion of the second hand (s), we can use the following formula:
h = (s/360) * 30
The second hand makes a full rotation of 360 degrees in one minute, so in 60 minutes (or one hour), it rotates 21,600 degrees. We know that during this time, the hour hand moves 30 degrees.
Therefore, the equation relating h and s is h = (s/360) * 30.
Equivalent ratios
Problem
Select three ratios that are equivalent to 8:5
Choose 3 answers:
A
16:10
B
50:80
C
48:30
D
32:20
E
64:35
Answer: Three equivalent ratios of 8 : 5 are 16 : 10, 24 : 15 and 32 : 20.
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST!
1) when a certain polynomial is divided by x+3, the quotient is x^2-3x+5 and the remainder is 6. what is the polynomial?
2) when a certain polynomial is divided by x-2, the quotient is x^2+4x-7 and the remainder is -4. what is the polynomial?
Which of the following represents vector vector u equals vector RS in linear form, where R (–25, 5) and S (–36, 11)?
v = –11i + 6j
v = 11i + 6j
v = 6i – 11j
v = –6i +11j
The vector V in linear form will be v = –11i + 6j i.e. A.
What exactly is a vector?In mathematics, a vector is a mathematical object that has both magnitude and direction. It is typically represented as an arrow in space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.
Now,
Vector RS can be represented as the difference between the coordinates of R and S:
RS = S - R
RS = (-36, 11) - (-25, 5)
RS = (-36 + 25, 11 - 5)
RS = (-11, 6)
To represent RS in linear form, we can use the components of the vector as coefficients of the basis vectors i and j:
RS = -11i + 6j
Therefore,
the correct option is v = -11i + 6j.
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Answer:
A is right
Step-by-step explanation:
Are the triangles similar? Yes or no
HELP PLSS ITS HW:))
please help me here mathematical literacy grade 12
1. The loan term of the truck is 5 years.
2. The contractor has to pay R30,801.67 per month towards the truck, including the insurance cover amount.
3. In in June 2022, the contractor owed the financer R669,050.10, excluding the insurance amount.
How to calculate the amount1. The loan term of the truck in years is calculated as follows:
Number of years = Loan term in months / 12
Number of years = 60 months / 12
Number of years = 5 years
Therefore, the loan term of the truck is 5 years.
2. Monthly repayments = Monthly instalment of the truck + Insurance premium
Monthly repayments = R22,301.67 + R8,500
Monthly repayments = R30,801.67
Therefore, the contractor has to pay R30,801.67 per month towards the truck, including the insurance cover amount.
3. Number of instalments paid = Loan term in months / 2
Number of instalments paid = 60 months / 2
Number of instalments paid = 30 months
The total amount of money owed to the financer excluding the insurance in June 2022 would be:
Total amount owed = Remaining instalments x Monthly instalment of the truck
Total amount owed = (Loan term in months - Number of instalments paid) x Monthly instalment of the truck
Total amount owed = (60 months - 30 months) x R22,301.67
Total amount owed = 30 months x R22,301.67
Total amount owed = R669,050.10
Therefore, in June 2022, the contractor owed the financer R669,050.10, excluding the insurance amount.
The significance of including an insurance cover when a contractor purchases a water tanker is to protect the asset from unforeseen circumstances such as accidents, theft, or damage. If the contractor did not have insurance, they would have to pay for any repairs or replacements out of pocket, which could be expensive and financially devastating. Insurance also provides peace of mind and allows the contractor to focus on their business operations without worrying about potential risks to their asset.
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Means and Mean Absolute Deviations of
Individual Times of Members of 4 times 400 meter Relay Track Teams
Team A
Team B
Mean
59.32 s
59.1 s
Mean Absolute Deviation
1.5 s
2.4 s
What is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B?
9% percent of Team B’s mean absolute deviation is the difference in the mean of the individual times of members.
What is Mean?The result of dividing the sum of a set of values by the total number of values in the set is mean.
The average distance between each observation and the mean is shown via a measure of variability known as the mean absolute deviation (MAD).
The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
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which mathematical symbols are used to indicate that the endpoints of an interval are not included in the graph of an inequality?
Answer:
The mathematical symbols used to indicate that the endpoints of an interval are not included in the graph of an inequality are "<" and ">" signs with a small circle or parenthesis next to them.
The symbol "<" with a circle or parenthesis on the right side indicates that the endpoint is not included, while the symbol ">" with a circle or parenthesis on the left side indicates that the endpoint is not included.
For example, the inequality x > 3 indicates that the variable x is greater than 3, but does not include 3 in its solution set. Similarly, the inequality y < -2 with a circle or parenthesis on the left side indicates that the variable y is less than -2, but does not include -2 in its solution set.
Step-by-step explanation:
9. A service station charges $195 for
two tires and installation. If the
installation portion of the bill is $23,
what is the price of one tire? Write
and solve an equation.
Answer:
it's 10 I think.you got to write the steps outWhich expression is equivalent to 36x6z2−−−−−−√36x6z2 when x>0x>0, and z>0z>0?
The equivalent expression of [tex]\sqrt{36x^6z^2[/tex] is option (B) [tex]6x^3z[/tex] . The expression [tex]\sqrt{36x^6z^2[/tex] represents the square root of the product of 36, x raised to the power of 6, and z raised to the power of 2.
What is square root ?
Square root is a mathematical operation that, when applied to a non-negative number, returns another non-negative number that, when multiplied by itself, gives the original number as a result.
The expression [tex]\sqrt{36x^6z^2[/tex] represents the square root of the product of 36, x raised to the power of 6, and z raised to the power of 2. To simplify this expression, we can use the following rules of exponents and radicals:
[tex]\sqrt{(a * b)} = \sqrt{a} *\sqrt{b[/tex]
[tex]\sqrt{(a^2)} = a[/tex] for all non-negative values of a
Using these rules, we can write:
[tex]\sqrt{36x^6z^2 }= \sqrt{(36 * x^6 * z^2)[/tex]
[tex]= \sqrt{(6^2 * (x^3)^2 * z^2)[/tex] (grouping factors with perfect square roots)
[tex]= 6 * x^3 * z[/tex] (simplifying the square root of the perfect square 6^2)
Therefore, the equivalent expression of [tex]\sqrt{36x^6z^2[/tex] is [tex]6x^3z[/tex]. This means that the square root of [tex]36x^6z^2[/tex] is equal to 6 times the product of x raised to the power of 3 and z.
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Use the Distributive Property to expand 7(6+x) 7 ( 6 + x ) .
Answer:
See below
Step-by-step explanation:
[tex]7(6+ x)[/tex] = [tex](7)(6) + (7)(x)[/tex]
= [tex]42 + 6x[/tex]
Calculate the mean and the population standard deviation for the data set, rounded to thousandths. {2, 3, 5, 0, 3, 2, 1, 1, 5, 7, 8, 5, 3}
SOMEONE PLEASE HELP
Rewrite the equation using the distributive property and solve for x.
5 ( x -1) = 25
please show all steps clearly if you answer.
When Mr. Farrell preheated his oven, the oven's temperature rose 3 degrees in 1 6 of a minute. At that rate, how much will the oven heat up in 1 minute?
The oven will heat up by 18 degrees in 1 minute at this rate.
What is the rate of change?
The term "rate of change" refers to how fast a quantity is changing with respect to time, or some other independent variable.
If the oven's temperature rose 3 degrees in 1/6 of a minute, we can find the rate of temperature increase by multiplying both sides by 6 to get:
3 degrees / (1/6 minute) = 18 degrees/minute
Hence, the oven will heat up by 18 degrees in 1 minute at this rate.
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a) Order the following values from smallest
to largest:
0.8, 0.4,
5
10'
7
10
b) Write a sentence to explain the method
you used.
PLEASE DO IT
I’ll give 25 points
Answer:
Step-by-step explanation 0.4 0.8 5 7 10, 10
Review the graph of function f(x), which is defined for –6 ≤ x ≤ 8. On a coordinate plane, a line goes from closed circle (negative 6, 6) to closed circle (2, negative 8). A line goes from open circle (2, 0) to closed circle (8, 6). Which one-sided limit does not exist? Limit of f (x) as x approaches 2 plus Limit of f (x) as x approaches 2 minus Limit of f (x) as x approaches negative 6 plus Limit of f (x) as x approaches negative 6 minus
The limit of f(x) as x approaches -6 from the positive side is 6.
When x gets closer to 2 on the positive side, we can see that the function seems to be heading towards a value of -8. As a result, f(x) has a limit of -8 as x approaches 2 from the positive side.
The function seems to be heading towards a value of 6 when x approaches 2 from the negative side. Hence, when x gets closer to 2 from the negative side, the limit of f(x) is 6.
The function seems to be getting closer to a value of 6 when x approaches -6 from the positive side. Hence, as x gets closer to -6 on the positive side, the limit of f(x) is equal to 6.
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a bag contains 3 red marbles and 4 blue marbles
one is taken from the bag and replaced
another marble is taken
work out the probability that the two marbles taken from the bag are the same colour
give your answer as a fraction
Answer:
When a marble is taken out from the bag and replaced, the probability of getting a red or blue marble on the first draw remains the same for the second draw. Therefore, we can use the multiplication rule of probability to calculate the probability of getting two marbles of the same color.
Let's denote the event of getting a red marble as R and the event of getting a blue marble as B. Then, the probability of getting two marbles of the same color can be calculated as follows:
Probability of getting two red marbles: P(R and R) = P(R) * P(R) = (3/7) * (3/7) = 9/49
Probability of getting two blue marbles: P(B and B) = P(B) * P(B) = (4/7) * (4/7) = 16/49
Therefore, the probability of getting two marbles of the same color is the sum of the probabilities of getting two red marbles and two blue marbles, which is:
P(same color) = P(R and R) + P(B and B) = 9/49 + 16/49 = 25/49
So the probability of getting two marbles of the same color is 25/49.
Step-by-step explanation:
determine the value of X
Answer:
"B"
Add all the sides together
Step-by-step explanation:
6. The height of Martin's rectangular door is 8
inches more than 3 times the width. If w
represents the width of the door, write an
expression
to represent the area of the door.
The expression that represents the area of the given door is (3w+8)w.
What are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.
A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.
This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)
So, we know that:
width = w
And we also know that:
length = 3w + 8
Now, the area formula is:
l*w
Insert values as follows:
l*w
(3w + 8)w
Therefore, the expression that represents the area of the given door is (3w+8)w.
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Which symbol correctly compares the two angles?
60° __ π/6
A. =
B. <
C. >
Answer:
c
Step-by-step explanation:
60>30 since pi is 180 ........
The equation of the line of best fit representing the data
on a scatter plot is y = 3.2x + 25. Based on the line of
best fit, which prediction is most reasonable for the
difference in y-values when the x-values are 20 and 35?
A. 48
B. 73
C. 88
D. 33
48
The line of best fit has the following equation
y = 3.2x + 25
Since the x-values are 20 and 35, we must enter these values into the equation and subtract them to determine the difference in the y-values:
y(20) - y(35) = (3.220 + 25) - (3.235 + 25)
y(20) - y(35) = (64 + 25) - (112 + 25)
y(20) - y(35) = 89 - 137
y(20) - y(35) = -48
For x-values of 20 and 35, 48 is the most logical prediction for the difference in y-values.
Thus, Option (A) 48 is the correct answer.
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In the picture does this represent a function??
Because,
It satisfies the vertical line test and represents a function.
What is function ?
Function can be defined in which it relates an input to output.
Based on the image you provided, it seems to represent a function since each input value (x-value) corresponds to a unique output value (y-value) and there is only one output value for each input value.
To verify if a graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. However, in this graph, for any vertical line drawn, it only intersects the graph at one point.
Hence, it satisfies the vertical line test and represents a function.
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If 2 similar regular hexagons have areas of 25√3 cm² and 16√3 cm² respectively. What is the scale factor from smaller to larger pentagon?
Answer:
The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.
In this case, we have two similar regular hexagons. Let x be the side length of the smaller hexagon, and y be the side length of the larger hexagon. Then, we have:
Area of smaller hexagon / Area of larger hexagon = (x^2 * 6 * sqrt(3)) / (y^2 * 6 * sqrt(3)) = x^2 / y^2
We are given the areas of the two hexagons:
x^2 * 6 * sqrt(3) = 16 * sqrt(3)
y^2 * 6 * sqrt(3) = 25 * sqrt(3)
Dividing the second equation by the first equation, we get:
(y^2 * 6 * sqrt(3)) / (x^2 * 6 * sqrt(3)) = 25 * sqrt(3) / (16 * sqrt(3))
Simplifying this expression gives:
y^2 / x^2 = 25 / 16
Taking the square root of both sides, we get:
y / x = 5 / 4
Therefore, the scale factor from the smaller hexagon to the larger hexagon is 5/4.
Please explain and show all of your work.
In Triangle LMO, T is the midpoint of LM, J is the midpoint of MO, and P is the midpoint of LO. Also, LT 9, JM = 12, and OL = 32.
What is the perimeter of the Triangle TJP?
Answer:
Step-by-step explanation:
We are given that T is the midpoint of LM, J is the midpoint of MO, and P is the midpoint of LO. This means that LT = TM, JO = OM, and LP = PO.
We can use this information to find the lengths of the sides of triangle LMO. Since T is the midpoint of LM, we have LT = TM = 9. Similarly, since J is the midpoint of MO, we have JO = OM = 12. Finally, since P is the midpoint of LO, we have LP = PO = (LO)/2 = 32/2 = 16.
Now, we can use the Pythagorean theorem to find the length of the third side, LM:
LM^2 = LT^2 + TM^2
LM^2 = 9^2 + 16^2
LM^2 = 337
LM = sqrt(337)
Therefore, the perimeter of triangle LMO is:
LM + MO + LO = sqrt(337) + 2(12) + 32
Perimeter = sqrt(337) + 56
To find the perimeter of triangle TJP, we need to find the lengths of the sides TJ, JP, and TP. Since T and J are midpoints of their respective sides, we know that TJ = 2(LT) = 18 and JP = 2(JO) = 24. To find TP, we can use the Pythagorean theorem:
TP^2 = TJ^2 + JP^2
TP^2 = 18^2 + 24^2
TP^2 = 900
TP = 30
Therefore, the perimeter of triangle TJP is:
TJ + JP + TP = 18 + 24 + 30
Perimeter = 72
Therefore, the perimeter of triangle TJP is 72.
Solve for X using the info below.
The value of x in the diagram is 12.5
What are similar shapes?Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors. Equal scale factors mean that the lengths of their corresponding sides have a matching ratio.
The ratio of the corresponding sides of similar shapes are equal.
Therefore;
3x/60 = 5x/8x
3x/60 = 5/8
300 = 24x
divide both sides by 24
x = 300/24
x = 12.5
therefore the value of x is 12.5
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Classify the triangle below as Right, Obtuse, or Acute
The triangles include:
4) Acute5) Obtuse6) Obtuse7) Right8) Right9) Obtuse10) ObtuseHow to classify triangles?
4) To determine if a triangle is right, obtuse, or acute, we need to use the Pythagorean Theorem to determine if the square of the longest side equals the sum of the squares of the other two sides.
Here, the longest side is 9, and the other two sides are 6 and 7.
9² = 6² + 7²
81 = 36 + 49
81 = 85
Since 81 is not equal to 85, the triangle is not a right triangle. To determine if it's obtuse or acute, we need to check the cosine of the largest angle using the Law of Cosines.
cos A = (b² + c² - a²) / 2bc
Let's choose 9 as side a, since it's the largest side:
cos A = (6² + 7² - 9²) / (84)
cos A = 0.048
Since cos A is positive, angle A is acute. Therefore, the triangle is acute.
5) Using the same process as above:
16² = 10² + 12²
256 = 100 + 144
256 = 244 + 12
Since 256 is greater than 244, the triangle is obtuse.
6) Again, using the same process as above:
(8√6)² = 8² + 16²
192 = 64 + 256
192 = 320
Since 192 is less than 320, the triangle is obtuse.
7) 29² = 20² + 21²
841 = 400 + 441
841 = 841
Since 841 is equal to 841, the triangle is a right triangle.
8) √73 is greater than 8 and 3, so it must be the largest side.
(√73)² = 8² + 3²
73 = 64 + 9
73 = 73
Since 73 is equal to 73, the triangle is a right triangle.
9) 12² = 8² + 10²
144 = 64 + 100
144 = 164 - 20
Since 144 is less than 164, the triangle is obtuse.
10) 15² = 9² + (3√34)²
225 = 81 + 306
225 = 387 - 162
Since 225 is less than 387, the triangle is obtuse.
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Triangle ABC is shown. Use the graph to answer the question. triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2 Determine the coordinates of the image if triangle ABC is translated 4 units down. A′(1, −6), B′(9, −6), C′(5, −2) A′(1, 2), B′(9, 2), C′(5, 6) A′(5, −2), B′(13, −2), C′(9, 2) A′(−3, −2), B′(5, −2), C′(1, 2)
The correct answer is A′(−3, −2), B′(5, −2), C′(1, 2). The coordinates of the original triangle ABC are (1, -2), (9, -2), and (5, 2). Therefore, the coordinates of the image are A′(−3, −2), B′(5, −2), C′(1, 2).
What are coordinates?Coordinates are used to describe a point in space or on a map. They are usually written as two numbers, which represent the position of the point on an x-axis and a y-axis. Coordinates can be used in a variety of ways, such as to describe the location of a specific object or to identify the boundaries of an area.
Triangle ABC is an example of a transformation in which the shape is shifted without changing its size or orientation. When a shape is translated, it is moved from one place to another without changing its size or orientation. In this case, the triangle is being translated 4 units down.
To calculate the new coordinates of the triangle, we need to subtract 4 from the y-coordinate of each of the vertices. The original coordinates of the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 from each of the y-coordinates, the new coordinates of the triangle are (1, −6), (9, −6), and (5, −2). This means that the new coordinates of the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).
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The cοrrect answer is A′(−3, −2), B′(5, −2), C′(1, 2). The cοοrdinates οf the οriginal triangle ABC are (1, -2), (9, -2), and (5, 2). Therefοre, the cοοrdinates οf the image are A′(−3, −2), B′(5, −2), C′(1, 2).
What are cοοrdinates?Cοοrdinates are used tο describe a pοint in space οr οn a map. They are usually written as twο numbers, which represent the pοsitiοn οf the pοint οn an x-axis and a y-axis. Cοοrdinates can be used in a variety οf ways, such as tο describe the lοcatiοn οf a specific οbject οr tο identify the bοundaries οf an area.
Triangle ABC is an example οf a transfοrmatiοn in which the shape is shifted withοut changing its size οr οrientatiοn. When a shape is translated, it is mοved frοm οne place tο anοther withοut changing its size οr οrientatiοn. In this case, the triangle is being translated 4 units dοwn.
Tο calculate the new cοοrdinates οf the triangle, we need tο subtract 4 frοm the y-cοοrdinate οf each οf the vertices. The οriginal cοοrdinates οf the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 frοm each οf the y-cοοrdinates, the new cοοrdinates οf the triangle are (1, −6), (9, −6), and (5, −2). This means that the new cοοrdinates οf the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).
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Suppose that 10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.
a. Let's consider your existing mortgage:
i. How much money did you pay as your down payment?
ii. How much money was your mortgage (loan) for?
iii. What is your current monthly payment?
iv. How much total interest will you pay over the life of the loan?
b. This year, you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $88,536 left to pay on your loan. Your house is now valued at $150,000.
i. How much of the loan have you paid off? (i.e., how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)
ii. How much money have you paid to the loan company so far?
iii. How much interest have you paid so far?
iv. How much equity do you have in your home (equity is value minus remaining debt)
i. The down payment is $11,000
ii. The mortgage (loan) was for $99,000.
iii. The current monthly payment is $471.15.
iv. Total interest is $169,334.00.
Down payment:The down payment is the initial payment made when purchasing a home, typically expressed as a percentage of the total purchase price.
Mortgage (loan):In the given problem, the mortgage (loan) is the amount of money borrowed to purchase the home, which is equal to the purchase price of the home minus the down payment.
Here we have
Problem 1:
10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.
The down payment was 10% of the purchase price of the home
=> Down payment = 10% of $110,000
= [10/100] × $110,000 = $11,000
∴ You will be paid $11,000 as your down payment.
Amount borrowed = the purchase price of the home - Down payment
=> Amount borrowed = $110,000 - $11,000 = $99,000
∴ Your mortgage (loan) was for $99,000.
To calculate the current monthly payment, use the formula for the monthly payment of a fixed-rate mortgage:
P = (A / D) x (r / 12)
Where:
A = amount borrowed
D = discount factor, i.e calculated as (1 - (1 + r / 12)⁻ⁿ)
r = monthly interest rate,
n = total number of payments,
=> P = ($99,000 /124.4) x 0.0075 = $471.15
∴ The current monthly payment is $471.15.
The formula for total interest = (P x n) - A
=> Total interest = ($471.15 x 360) - $99,000 = $169,334.00
∴ You will pay a total of $169,334.00 in interest over the life of the loan.
Therefore,
i. The down payment is $11,000
ii. The mortgage (loan) was for $99,000.
iii. The current monthly payment is $471.15.
iv. Total interest is $169,334.00.
Problem 2
This year, you check your loan balance. You see that you still have $88,536 left to pay on your loan. Your house is now valued at $150,000.
i. Amount paid off = Original loan amount - Current loan balance
Original loan amount = $99,000
Current loan balance = $88,536
Amount paid off = $99,000 - $88,536
Amount paid off = $10,464
∴ you have paid off $10,464 of the loan.
ii. Total paid = Monthly payment x Number of payments
P = ($99,000 / 207.483) x 0.0075
P ≈ $471.15
The number of payments is the number of months since you took out the loan. Since the loan was taken out 10 years ago, or 120 months ago, the number of payments is 120.
Total paid = $471.15 x 120
Total paid = $56,538
∴ you have paid $56,538 to the loan company so far.
iii. To determine how much interest you have paid so far, we need to subtract the amount paid off from the total amount paid:
Interest paid = Total paid - Amount paid off
Interest paid = $56,538 - $10,464
Interest paid = $46,074
∴ you have paid $46,074 in interest so far.
iv. Equity = Current value of the home - Current loan balance
Equity = $150,000 - $88,536
Equity = $61,464
∴ you have $61,464 of equity in your home.
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