Answer:
x=8
Step-by-step explanation:
48=5(2x-7)+3
Use the distributive property
48=10x-35+3
Combine like terms
48=10x-32
Add 32 to both sides to cancel out the negative 32
80=10x
x=8
Answer:
x = 8
Step-by-step explanation:
Step 1: Write equation
48 = 5(2x - 7) + 3
Step 2: Solve for x
Distribute 5: 48 = 10x - 35 + 3Combine like terms: 48 = 10x - 32Add 32 to both sides: 80 = 10xDivide both sides by 10: 8 = xRewrite: x = 8Step 3: Check
Plug in x to verify it's a solution.
48 = 5(2(8) - 7) + 3
48 = 5(16 - 7) + 3
48 = 5(9) + 3
48 = 45 + 3
48 = 48
the standard form of -36/-216
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\frac{-36}{-216} \\=\frac{36}{216} \\=\frac{1}{6}[/tex]
Two companies offer jane sales position. Company a pays $3,000 per month plus $250 per car sold.. Company B pays 2,500 per month plus $350 per car sold. Which equation could be used to determine the number of cars sold in a month, x, that would result in the same total income from each company?
Given :
Two companies offer jane sales position. Company a pays $3,000 per month plus $250 per car sold.. Company B pays 2,500 per month plus $350 per car sold.
To Find :
Which equation could be used to determine the number of cars sold in a month, x, that would result in the same total income from each company.
Solution :
Let, x car are sold for same income.
Mathematical equation of company one :
[tex]T_1 =3000+250x[/tex]
Mathematical equation of company two :
[tex]T_2 =2500+350x[/tex]
For same income :
[tex]T_1=T_2\\\\3000 + 250x = 2500 + 350x\\\\100x = 500\\\\x=5[/tex]
So, for same total income from each company the number of cars sold in a month should be 5.
Hence, this is the required solution.
Membership to a music club costs $165. Members
pay $25 per music lesson and nonmembers pay $40
per music lesson. How many music lessons would
have to be taken for the cost to be the same for
members and nonmembers?
plz my time is running out
Answer:
11 music lessons.
Step-by-step explanation:
We know that membership costs $165 and members pay $25 per music lesson.
So, we can write the following expression:
[tex]165+25m[/tex]
The 165 represents the one-time membership fee and the 25m represents the cost for m music lessons.
We know that non-members pay no membership fee but their cost per lesson is $40. So:
[tex]40m[/tex]
Represents the cost for non-members for m music lessons.
We want to find how many music lessons would have to be taken for the cost to be the same for both members and non-members. So, we can set the expressions equal to each other:
[tex]165+25m=40m[/tex]
And solve for m. Let's subtract 25m from both sides:
[tex]165=15m[/tex]
Now, divide both sides by 15:
[tex]m=11[/tex]
So, at the 11th music lesson, members and non-members will pay the same.
Further Notes:
This means that if a person would only like to take 10 or less lessons, the non-membership is best because there is no initial fee.
However, if a person would like to take 12 or more lessons, than the membership is best because the membership has a lower cost per lesson than the non-membership.
And we're done!
4. Prove that to every A E L (R", R¹) corresponds a unique y € R such that Ax = x.y. Prove also that || A|| = |y|. Hint: Under certain conditions, equality holds in the Schwarz inequality.
For every matrix A in the space of linear transformations from [tex]R^n[/tex] to [tex]R^1[/tex], there exists a unique vector y such that Ax = x.y
The norm of A is equal to the absolute value of y. This is proven using the Schwarz inequality.
Let A be a matrix in the space of linear transformations from [tex]R^n[/tex] to [tex]R^1[/tex]. For any vector x in [tex]R^n[/tex], we can define Ax as a dot product between A and x. Let y be a vector in [tex]R^1[/tex] such that Ax = x.y for all x in [tex]R^n[/tex] . This means that the dot product of A and x yields a scalar multiple of x, where the scalar is y.
To prove uniqueness, assume there are two vectors [tex]y_{1}[/tex] and [tex]y_{1}[/tex] in [tex]R^1[/tex] such that Ax = x.[tex]y_{1}[/tex] and Ax = x.[tex]y_{2}[/tex] for all x in [tex]R^n[/tex]. Then, x.[tex]y_{1}[/tex] = x.[tex]y_{2}[/tex] for all x in [tex]R^n[/tex], which implies [tex]y_{1}= y_{2}[/tex]. Therefore, there exists a unique vector y such that Ax = x.y.
To prove that ||A|| = |y|, we can use the Schwarz inequality. The Schwarz inequality states that for any vectors u and v in [tex]R^n[/tex], |u.v| ≤ ||u|| * ||v||, with equality holding if and only if u and v are linearly dependent. Applying this inequality to the vectors A and x, we have |Ax.x| ≤ ||Ax|| * ||x||. Since Ax = x.y and ||Ax|| = ||x.y|| = |y| * ||x||, the inequality becomes |x.y.x| ≤ |y| * [tex]||x||^2[/tex]. Since the dot product x.y.x is equal to y * (x.x) = y * [tex]||x||^2[/tex], we have |y| *[tex]||x||^2[/tex] ≤ |y| * [tex]||x||^2[/tex], which holds with equality. Hence, ||A|| = |y|.
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Instructions = a. Perform a horizontal percent of base year analysis of WestJet's income statement and balance sheet, assuming 2013 is the base year. b. Using the analyses you prepared in part (a), id
The task requires performing a horizontal percent of base year analysis on WestJet's income statement and balance sheet, considering 2013 as the base year. This analysis will help identify the trends and changes in financial figures over the specified period.
To conduct a horizontal percent of base year analysis, we compare the financial figures of subsequent years to the base year and calculate the percentage change. Here's how the analysis can be performed:
a. Income Statement Analysis:
Calculate the percentage change in each line item of the income statement by comparing it to the corresponding figure in the base year (2013).
For example, if the revenue in 2013 is $100 and it increases to $120 in 2014, the percentage change would be [(120 - 100) / 100] * 100 = 20%.
Perform this calculation for each line item in the income statement to determine the percentage change for each year.
b. Balance Sheet Analysis:
Similar to the income statement analysis, calculate the percentage change in each line item of the balance sheet by comparing it to the corresponding figure in the base year (2013).
For example, if the total assets in 2013 are $500 and they increase to $600 in 2014, the percentage change would be [(600 - 500) / 500] * 100 = 20%.
Perform this calculation for each line item in the balance sheet to determine the percentage change for each year.
Using the analyses prepared in part (a), we can identify the trends and changes in WestJet's income statement and balance sheet over the specified period. By comparing the percentage changes, we can determine which line items have shown significant growth or decline compared to the base year. This analysis helps in assessing the company's financial performance, identifying areas of strength or weakness, and making informed decisions based on the observed trends.
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There are 125 passengers in the first carriage, 150 passengers in the second carriage and 175 passengers in the third carriage, and so on in an arithmetic sequence. What’s the total number of passengers in the first 7 carriages
Answer:
1400
Step-by-step explanation
First I made a list of all of the first 7 carriages, so that's 125, 150, 175, 200, 225, 250, and 275. After adding those you get 1400.
1. While raking leaves, a woman applies an input force of 32 N to a rake. The rake has an output force of 16 N. What is the mechanical advantage of the rake?
2. A carpenter turns a handle to adjust a saw blade. The input work is 55 J and the output work is 51 J. What is the efficiency of the blade adjuster?
1. the mechanical advantage of the rake is 0.5. 2. the efficiency of the blade adjuster is approximately 92.73%.
1. The mechanical advantage of a simple machine is determined by the ratio of the output force to the input force. In this case, the woman applies an input force of 32 N to the rake, and the rake exerts an output force of 16 N.
The mechanical advantage (MA) can be calculated as MA = Output Force / Input Force.
Using the given values, we can substitute them into the formula:
MA = 16 N / 32 N = 0.5.
Therefore, the mechanical advantage of the rake is 0.5.
Explanation:
The mechanical advantage represents the amplification of force achieved by using a machine. In this case, the mechanical advantage of 0.5 means that the rake reduces the input force by half to produce the output force. It indicates that for every 1 unit of input force applied by the woman, the rake generates 0.5 units of output force.
2. Efficiency is a measure of how effectively a machine converts input work to output work. It is calculated as the ratio of output work to input work, expressed as a percentage.
The efficiency (η) can be calculated using the formula: Efficiency = (Output Work / Input Work) * 100%.
Given that the input work is 55 J and the output work is 51 J, we can substitute these values into the formula:
Efficiency = (51 J / 55 J) * 100% ≈ 92.73%.
Therefore, the efficiency of the blade adjuster is approximately 92.73%.
Explanation:
Efficiency quantifies the effectiveness of a machine in converting the input energy into useful output energy. In this case, the blade adjuster converts 51 J of input work into 51 J of output work. The efficiency of approximately 92.73% indicates that the blade adjuster is relatively efficient, as a high percentage of the input work is effectively converted into useful output work.
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a number cube with faces labeled from to will be rolled once. the number rolled will be recorded as the outcome. give the sample space describing all possible outcomes. then give all of the outcomes for the event of rolling an odd number. if there is more than one element in the set, separate them with commas.
The probability of rolling an odd number is 1/2, assuming that the number cube is fair.
The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is rolling a number cube once and recording the outcome. Since the number cube has six faces labeled from 1 to 6, the sample space can be represented as:
S = {1, 2, 3, 4, 5, 6}
The event of rolling an odd number consists of the outcomes 1, 3, and 5.
Therefore, the set of all outcomes for the event of rolling an odd number is: {1, 3, 5}
The probability of rolling an odd number can be found by adding the probabilities of the individual outcomes in the event:
{P(odd)} = P(1) + P(3) + P(5) = 1/6 + 1/6 + 1/6 = 3/6 = 1/2
Therefore, the probability of rolling an odd number is 1/2.
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Find the Distance between (-1,4) and (3,1)
Answer:
5. This question is hard to explain, sorry.
What is this number in standard notation? 9.41 x 106
Answer:
9997.46
Step by step Explanation
Q. 2) (10 p.) Answer each of the following: (a) A matrix polynom is given by P(x) = x². By considering the 2 by 2 matrix as A = - 1, 0 (b) For a given matrix A = [2], calculate A-, where k is any integer. -2. find P(A).
(a) The matrix polynomial P(x) = x² can be evaluated by substituting the given 2 by 2 matrix A = [-1, 0; -2, 1] into P(x).
(b) To calculate A^-, where k is any integer, we need to find the inverse of the matrix A. Additionally, P(A) can be obtained by substituting matrix A into the matrix polynomial P(x) = x².
(a) To evaluate the matrix polynomial P(x) = x² using the given 2 by 2 matrix A = [-1, 0; -2, 1], we substitute A into P(x):
P(A) = A² = [-1, 0; -2, 1]² = [(-1)(-1) + (0)(-2), (-1)(0) + (0)(1); (-2)(-1) + (1)(-2), (-2)(0) + (1)(1)] = [1, 0; 0, -3].
(b) To calculate A^-, where k is any integer, we need to find the inverse of the matrix A = [2, -2; -2, 4]. The inverse of a 2 by 2 matrix can be found using the formula:
A^-1 = (1/det(A)) * adj(A),
where det(A) is the determinant of A and adj(A) is the adjugate of A. Calculating the determinant and adjugate of A, we have:
det(A) = (2)(4) - (-2)(-2) = 12 - 4 = 8,
adj(A) = [4, 2; 2, 2].
Therefore, A^-1 = (1/8) * [4, 2; 2, 2] = [1/2, 1/4; 1/4, 1/4].
To find P(A), we substitute A into the matrix polynomial P(x) = x²:
P(A) = A² = [2, -2; -2, 4]² = [2, -2; -2, 4] * [2, -2; -2, 4] = [4 - 4, -4 + 8; -4 + 4, 4 + 16] = [0, 4; 0, 20].
Therefore, A^-1 = [1/2, 1/4; 1/4, 1/4] and P(A) = [0, 4; 0, 20].
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During the current year, merchandise is sold for $114,000 cash and $548,100 on account. The cost of the goods sold is $423,700. What is the amount of the gross profit? $fill in the blank 1
During the current year, merchandise was sold for $662,100. Of this amount, $114,000 was cash sales and $548,100 was on account. The cost of goods sold was $423,700. Therefore, the gross profit was $238,400.
The gross profit is calculated by subtracting the cost of goods sold from the total sales. The cost of goods sold is the direct cost of producing the goods that were sold. It includes the cost of materials, labor, and overhead.
The gross profit is an important measure of a company's profitability. It shows how much money the company makes from its core business activities, before deducting other expenses.
In this case, the company's gross profit margin is 35.8%. This means that for every $100 of sales, the company makes $35.80 in gross profit. A high gross profit margin is generally considered to be a sign of a healthy business.
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if there's 2,003 snakes currently and there's a constant rate of 100 per year what would be the equation for the population
Answer: The equation would be P(t) = 100t + 2003
Step-by-step explanation: The equation for the population of snakes over time would be P(t) = 100t + 2003, where P represents the population of snakes and t represents the time in years. The initial population of snakes is 2003, and the population increases by 100 snakes per year.
Therefore, after t years, the population of snakes would be 100t more than the initial population of 2003.
Verify if f(x) = 1/2x - 2 and g(x) = 2x + 4 are inverses.
Answer:
Step-by-step explanation:
Try using g(x)
Let g(x) = y
y = 2x + 4
Interchange x and y
x = 2y + 4
Subtract 4 from both sides
x - 4 = 2y
Divide by 2
x/2 - 4/2 = 2y/2
y = x/2 - 2
This is exactly what f(x) is
So g(x) and f(x) are inverses.
On simplifying (-3y2 − 8) − (-5y2 + 1), we get
Answer:
-3y2-8+5y2-1=
2y2-9
Step-by-step explanation:
Answer:
[tex]\huge{\boxed{\sf{ 2y^{2} - 9 }}}[/tex]
Step-by-step explanation:
[tex]( - 3y^{2} - 8 ) - ( - 5y^{2}+ 1 )[/tex]
While subtracting , sign of each term of the second expression changes.
⇒[tex]- 3y^{2} - 8 + 5y^{2} - 1[/tex]
Combine like terms : [tex]-3y^{2}[/tex] and [tex]5y^{2}[/tex]
Like terms are those which have the same base.
⇒[tex]2y^{2} - 8 - 1[/tex]
Remember : The negative integers are always added but posses the negative ( - ) sign.
⇒[tex]2y^{2} - 9[/tex]
Hope I helped!
Best regards !
-[tex]\sf{ TheAnimeGirl}[/tex]
Anyone know the answer ???
Answer:
The answer to what?
Step-by-step explanation:
‼️WILL LIST BRAINLIEST ‼️
Answer:
5/6
Step-by-step explanation:
-3/4 * - 10/9
A negative times a negative is a positive
3/4 * 10/9
Rewriting
3/9 * 10/4
1/3 * 5/2
Multiplying across
5/6
How do the side lengths of polygon ABCD compare with those of the translated images? What can you say about preservation of the measurements of side lengths when a figure is translated?
Answer: The side links of polygons ABCD are equal to corresponding side lengths in the translated images. this means that lengths of sides of the polygon are preserved as the figure is translated in any direction.
Suppose a baseball is thrown at 89 miles per hour. The ball will travel 324 feet when hit by a bat swung at 51 miles per hour and will travel 444 feet when hit by a boat swung at 81 miles per hour. Let y be the number of feet traveled by the ball when hit by a bat swung at x miles per hour. How much farther will a ball travel for each mile-per-hour increase in the speed of the bat?
Given:
Baseball is thrown at 89 miles per hour.
The ball will travel 324 feet when hit by a bat swung at 51 miles per hour.
It will travel 444 feet when hit by a boat swung at 81 miles per hour.
To find:
The addition distance travelled by the ball if the speed of bat increased by 1 unit.
Step-by-step explanation:
Let y be the number of feet traveled by the ball when hit by a bat swung at x miles per hour.
The ball will travel 324 feet when hit by a bat swung at 51 miles per hour. So, the point is (51,324).
It will travel 444 feet when hit by a boat swung at 81 miles per hour. So, the point is (81, 444).
Equation of line passes through two points is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-324=\dfrac{444-324}{81-51}(x-51)[/tex]
[tex]y-324=\dfrac{120}{30}(x-51)[/tex]
[tex]y-324=4(x-51)[/tex]
[tex]y-324=4x-204[/tex]
Add 324 on both sides.
[tex]y=4x-204+324[/tex]
[tex]y=4x+120[/tex]
Using the slope intercept form,
[tex]y=mx+b[/tex]
where, m is slope.
The slope of equation [tex]y=4x+120[/tex] is 4. It means, the ball will travel 4 feet farther for each mile-per-hour increase in the speed of the bat.
Jackson can swim 38 laps in 95 minutes. Write an equation relating the laps swam s to the number of minutes m. At this rate, how many laps can he swim in 115 minutes?
Answer:
46 laps
Step-by-step explanation:
Set up a ratio:
38/95 = s/115
cross multiply
4370 = 95s
divide both sides by 95
s= 46
The sum of 3 consecutive even integers is 18
Answer:
4,6,8
Step-by-step explanation:
Let x = 1st even integer
x+2 =2nd even integer
x+4 =3nd even integer
x+ x+2 + x+4 = 18
Combine like terms
3x+6 = 18
Subtract 6 from each side
3x+6-6=18-6
3x= 12
Divide by 3
3x/3 =12/3
x = 4
x+2 = 6
x+4 = 8
What is a coefficient in this equaiton?
3x + 2 = -10
Answer:
3 is the coefficient
Step-by-step explanation:
3x + 2 = -10
The coefficient is the number that is multiplied by the variable
3 is the coefficient
Answer:
3
Step-by-step explanation:
the 'a' coefficient is 3
3 is the number infront of x (the first one)
a coefficient is the number infront of the unknown value
10x+4x-1=0
10= coefficient a
4= coefficient b
-1= coefficient c
Which situation fits the following Inequality 7x+15≥50
Answer: x ≥ 5
---------------------
-3x -4.6 = 5.9
x = ?
Answer:
x=-3.5
Step-by-step explanation:
-3x=10.5 divide both sides by -3
Answer:
x = -3.5
Step-by-step explanation:
-3x - 4.6 = 5.9 ( add 4.6 on both sides)
-3x = 10.5 (divide by -3 on both sides)
x = -3.5
can someone please tell me the answer :(
Answer:
A
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
-18+-12+-6=-36
please help im using all my points!!
Zachary purchased a computer for $1600 on a payment plan. Two months after he purchased the computer, his balance was $1310.Three months after he purchased the computer, his balance was $1165. What is an equation that models the balance y after x months?
Answer: Three months after he purchased the computer, his balance was $1,350.
Step-by-step explanation:
The equation that models the balance y after x months will be: y = -145x + 1600.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that Zachary purchased a computer for $1600 on a payment plan.
Then two months after he purchased the computer, his balance was $1310. Three months after his balance was $1165.
Equation;
Month Balance
0 1600
2 1310
3 1165
Slopes:
(1600 - 1310) / 2 = 290/ 2 = 145
Hence,
y = -145x + 1600
Therefore the equation is; y = -145x + 1600.
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Quiz 3
The following data points represent the number of remote controllers each student in Tria's video game
club owns.
Sort the data from least to greatest.
0
0
0
1
2
2
4
5
7
8
10
Find the interquartile range (IQR) of the data set.
remote controllers
A
Report a problem
The interquartile range (IQR) of the data set is 7.To find the interquartile range (IQR) of a data set, we need to first determine the values of the first and third quartiles.
The first quartile (Q1) represents the 25th percentile of the data, while the third quartile (Q3) represents the 75th percentile of the data. We can find these values by first sorting the data set in ascending order:
0, 0, 0, 1, 2, 2, 4, 5, 7, 8, 10
Next, we can find the median (Q2) of the entire data set, which is the value that separates the lower 50% of the data from the upper 50%:
0, 0, 0, 1, 2, | 2, 4, 5, 7, 8, 10
Q2 = 2
Now we can find Q1 and Q3. To find Q1, we take the median of the lower half of the data set:
0, 0, 0, | 1, 2,
Q1 = 0
To find Q3, we take the median of the upper half of the data set:
2, 4, 5, 7, 8, 10
Q3 = 7
Finally, we can calculate the interquartile range (IQR) as the difference between Q3 and Q1:
IQR = Q3 - Q1
= 7 - 0
= 7
Therefore, the interquartile range (IQR) of the data set is 7.
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Answer: 7
Step-by-step explanation:
You just bought a new drone. You are standing in the middle of a park flying it, and know that you are 1500 feet from the building you live in. You also know that the building you live in is 150 feet tall. You decide you do not want to carry the drone back with you and can land it on the roof of your building instead. How far would your drone need to fly to go in a straight line from your current position to the roof of your building? Also, what angle should your drone take in its flight path?
To land the drone on the roof of the building, it would need to fly approximately 1505.35 feet in a straight line. The angle between the ground and the drone's flight path would be approximately 5.74 degrees.
To determine the distance the drone needs to fly, we can use the Pythagorean theorem. The horizontal distance between your current position in the park and the building is given as 1500 feet, and the height of the building is 150 feet. We can consider this as a right-angled triangle, with the horizontal distance as the base and the height of the building as the perpendicular side.
Using the Pythagorean theorem, we can find the hypotenuse (flight distance) of the triangle, which represents the straight-line distance the drone needs to travel. The equation is:
hypotenuse^2 = base^2 + perpendicular^2
Substituting the values, we get:
hypotenuse^2 = 1500^2 + 150^2
hypotenuse^2 = 2250000 + 22500
hypotenuse^2 = 2272500
Taking the square root of both sides, we find:
hypotenuse ≈ √2272500 ≈ 1505.35 feet
Therefore, the drone would need to fly approximately 1505.35 feet in a straight line to reach the roof of your building.
To determine the angle of the flight path, we can use trigonometry. The angle (θ) can be calculated using the tangent function:
tan(θ) = perpendicular/base
Substituting the values, we get:
tan(θ) = 150/1500
tan(θ) = 0.1
Taking the inverse tangent (arctan) of both sides, we find:
θ ≈ arctan(0.1) ≈ 5.74 degrees
Hence, the drone should take an angle of approximately 5.74 degrees in its flight path to reach the roof of your building.
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You plan to purchase a house for 12.5 million baht, using a 30-year mortgage. You will make a down payment of 15 percent of the purchase price and you will not pay off the mortgage early. Ignore taxes in your analysis. Your bank offers you the following two options for payment.
Option 1: Mortgage rate of 7.25 percent and zero points.
Option 2: Mortgage rate of 6.75 percent and 4 points.
You would choose option ------- (1 or 2) because the Net Present Value of choosing option 2 is------ . (The answer can be negative. Do not round intermediate calculations and round your answer to two decimal places, e.g., 32.16.)
Option 2 has a lower NPV and thus should be chosen as it results in less total payment and better savings. Hence, you would choose option 2 as the Net Present Value of choosing option 2 is -9,903,615.48.
Given:
Purchase price = 12.5 million baht
Down payment = 15%30-year mortgage
We have to calculate the option which is best for us.
Option 1: Mortgage rate = 7.25%
Option 2:Mortgage rate = 6.75%
(a) Monthly Payment of Option 1:
Loan Amount = 12.5 * (100-15)%
= 10,625,000 baht
n = 30 * 12
= 360
i = 7.25%/12
= 0.006042857
Yearly Interest Paid = i * 10,625,000
= 64,515.48 baht
Monthly Interest Paid = 64,515.48 / 12
= 5,376.29 baht
EMI =[tex][P x R x (1+R)^n] / [(1+R)^n-1][/tex]
where P = Loan Amount, R= Interest Rate per month, n= total number of payments.
EMI = [tex][10,625,000 x 0.006042857 x (1+0.006042857)^360] / [(1+0.006042857)^360-1][/tex]
EMI = 69,677.31 baht
(b) Monthly Payment of Option 2:
Loan Amount = 12.5 * (100-15)%
= 10,625,000 baht
n = 30 * 12 = 360
i = 6.75%/12 = 0.005625
Yearly Interest Paid = i * 10,625,000
= 59,765.63 baht
Monthly Interest Paid = 59,765.63 / 12
= 4,980.47 baht
Point cost = 4% of Loan Amount
= 10,625,000 x 4/100
= 425,000 baht
Loan Amount after Deducting Points = 10,625,000 - 425,000
= 10,200,000 baht
EMI = [tex][P x R x (1+R)^n] / [(1+R)^n-1][/tex]
where P = Loan Amount, R= Interest Rate per month, n= total number of payments.
EMI =[tex][10,200,000 x 0.005625 x (1+0.005625)^360] / [(1+0.005625)^360-1][/tex]
EMI = 66,128.92 baht
(c) We have to calculate the NPV of the payments to decide which option is better.
We use the formula to calculate NPV:-
NPV = - [tex][B + (PMT / i) * (1 - (1 + i)^-n)] / ((1 + i)^t)[/tex]
Where B = amount borrowed, PMT = monthly payment, i = interest rate, n = total number of payments, t = year.
NPV =[tex]- [10625000 + (69677.31 / 0.006042857) * (1 - (1 + 0.006042857)^-360)] / ((1 + 0.006042857)^30)[/tex]
= -9,892,571.85 baht
NPV = [tex]- [10200000 + (66128.92 / 0.005625) * (1 - (1 + 0.005625)^-360)] / ((1 + 0.005625)^30)[/tex]
= -9,903,615.48 baht
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