The difference in payments from year 5 to year 6 is approximately $369.32 for the 5/1 ARM mortgage.
To calculate the payment difference from year 5 to year 6 for a 5/1 ARM (Adjustable Rate Mortgage) with a 3/12 cap structure, we need to understand how the ARM works and how the caps affect the adjustment.
1. Initial Mortgage Parameters :
- Loan Amount: $265,000
- Interest Rate: 5.25%
- Term: 20 years
2. Adjustment Frequency : The 5/1 ARM adjusts after the initial 5-year fixed period, then annually.
3. Cap Structure :
- Initial Adjustment Cap: 3%
- Subsequent Adjustment Cap: Each year after the initial adjustment, the rate can adjust up to 3% from the previous rate.
4. Calculation Steps :
a. Calculate the initial monthly payment using the loan amount, interest rate, and term.
b. Determine the new interest rate for year 6 based on the cap structure.
c. Calculate the monthly payment for year 6 with the new interest rate.
d. Find the difference between the payments from year 5 to year 6.
Let's start the calculations:
a. Calculate the initial monthly payment using the loan amount, interest rate, and term. We'll use the formula for a fixed-rate mortgage:
[tex]\[ P = \frac{P_r \cdot A}{1 - (1 + r)^{-n}} \][/tex]
Where:
- [tex]\( P \)[/tex] = Monthly Payment
- [tex]\( P_r \)[/tex] = Periodic Interest Rate (annual rate divided by 12)
- [tex]\( A \)[/tex] = Loan Amount
- [tex]\( r \)[/tex] = Periodic Interest Rate
- [tex]\( n \)[/tex] = Total number of payments (loan term in years multiplied by 12)
For the initial fixed period of 5 years:
[tex]\[ P_r = \frac{5.25\%}{12} = 0.004375 \][/tex]
[tex]\[ n = 20 \times 12 = 240 \][/tex]
Plugging these values into the formula:
[tex]\[ P = \frac{0.004375 \cdot 265000}{1 - (1 + 0.004375)^{-240}} \][/tex]
[tex]\[ P \approx 1645.80 \][/tex]
So, the initial monthly payment is approximately $1,645.80.
b. Determine the new interest rate for year 6 :
- The initial rate can adjust up to 3% in year 6.
- So, the new interest rate could be up to \( 5.25\% + 3\% = 8.25\% \).
c. Calculate the monthly payment for year 6 :
- Use the formula for the monthly payment again with the new interest rate:
[tex]\[ P_r = \frac{8.25\%}{12} = 0.006875 \][/tex]
Plugging into the formula:
[tex]\[ P = \frac{0.006875 \cdot 265000}{1 - (1 + 0.006875)^{-240}} \][/tex]
[tex]\[ P \approx 1985.09 \][/tex]
So, the monthly payment for year 6 is approximately $1,985.09.
d. Find the difference in payments from year 5 to year 6:
[tex]\[ Difference = Payment_{Year6} - Payment_{Year5} \][/tex]
[tex]\[ Difference = 1985.09 - 1645.80 \][/tex]
[tex]\[ Difference \approx 339.29 \][/tex]
So, the difference in payments from year 5 to year 6 is approximately $339.29.
Therefore, the closest answer is C. $369.32 .
a game is played where 26 tiles are in a bag. each tile has a different letter of the alphabet on it. if you draw 5 letters what is the probability of the letters being m-u-s-i-c in order if there is no replacement?
The probability of drawing the letters M-U-S-I-C in order from a bag of 26 tiles without replacement is approximately 0.000207.
Explanation:The probability of drawing the letters M-U-S-I-C in order from a bag of 26 tiles without replacement can be calculated as follows:
First, we need to determine the total number of ways to draw 5 tiles from 26, which is represented by the combination formula: C(26,5) = 26! / (5! * (26-5)!).Next, we need to determine the number of ways to draw the letters M-U-S-I-C in order. Since there is only 1 M, 1 U, 1 S, 1 I, and 1 C in the bag, the number of ways to draw these 5 letters in order is 1.Finally, we divide the number of ways to draw the letters M-U-S-I-C in order by the total number of ways to draw 5 tiles from 26 to get the probability: P = 1 / C(26,5).Using a calculator or computer program, the probability can be calculated to approximately 0.000207.
Final answer:
The probability of drawing the letters 'M-U-S-I-C' in order from a bag of 26 alphabetic tiles without replacement is calculated by multiplying the individual probabilities of drawing each letter consecutively, starting with 1/26 and decreasing with each draw.
Explanation:
The question involves calculating the probability of drawing a specific sequence of letters from a bag containing all the letters of the alphabet without replacement. Here's how to calculate it step by step:
The probability of drawing the letter 'M' first is 1/26 since there are 26 letters and only one 'M'.
After drawing 'M', the probability of drawing 'U' is 1/25 because there are now 25 letters remaining.
Following this pattern, the probability of then drawing 'S' is 1/24, 'I' is 1/23, and 'C' is 1/22.
To find the combined probability of drawing 'M-U-S-I-C' in that order, multiply these probabilities together: (1/26) * (1/25) * (1/24) * (1/23) * (1/22).
The final calculation gives us the probability of the sequence occurring without any tiles being replaced.
During a construction project, heavy rain filled construction cones with water. The diameter of a cone is 12 in. and the height is 27 in.
What is the volume of the water that filled one cone?
Enter your answer as a decimal in the box. Use 3.14 for pi.
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Solve these simultaneous equations:
5x+2y=24 and 4x+3y=10
To solve the simultaneous equations 5x+2y=24 and 4x+3y=10, we use the elimination method, leading to a solution of x = 7.43 and y = -6.575.
To solve the simultaneous equations 5x+2y=24 and 4x+3y=10, we can use the method of elimination or substitution. Here, we will solve it using the elimination method.
Multiply the first equation by 3 and the second equation by 2 to make the coefficients of y equal in magnitude. This gives us 15x + 6y = 72 and 8x + 6y = 20.
Subtract the second new equation from the first to eliminate y. This gives 7x = 52.
Divide by 7 to solve for x, which gives x = 52 / 7 or x = 7.43 (approximately).
Substitute x = 7.43 back into one of the original equations to solve for y. Using the first equation, 5(7.43) + 2y = 24, we get 2y = 24 - 37.15, which simplifies to 2y = -13.15, and finally y = -6.575.
Therefore, the solution to the simultaneous equations is x = 7.43 and y = -6.575.
an architect created plans for a house using a scale factor of 1:16 . In the plans, the floor of the house has an area of 7 square feet. What is area of the floor in the actual house?
Answer:
The answer above me is correct
Step-by-step explanation:
Cause he big brain
How will buying auto insurance help you?
I WANT DIAGRAM
A vertical tower subtends a right angle on the top of 10m high flagstaff.if distance between them is 20m,find the height of the tower
Which of the six trigonometric functions do not depend on the value of r?
Suppose the probability that a randomly selected man, aged 55-59, will die of cancer during the course of the year is startfraction 300 over 100 comma 000 endfraction 300 100,000. how would you find the probability that at least 1 man out of 1,000 of this age will die of cancer during the course of the year?
Final answer:
To assess the likelihood of at least one cancer death among 1,000 men, calculate the probability none die and subtract from one. The actuarially fair premiums for men with and without family cancer history are different, but when combined for the whole group, there's a risk of adverse selection affecting the company.
Explanation:
To find the probability that at least one man out of 1,000 aged 55-59 will die of cancer in a year, given that the probability for any one man is 300/100,000, we first find the probability that no man dies of cancer and then subtract this from 1 (the certainty). The probability that a randomly chosen man will not die from cancer in the year is 1 - 300/100,000 = 99,700/100,000.
The probability that all 1,000 men do not die of cancer is (99,700/100,000)^1,000. Subtracting this from 1 gives us the probability that at least one man out of 1,000 will die of cancer in the year:
1 - (99,700/100,000)^1,000
For the life insurance question, to calculate the actuarially fair premium for each group, we use the probability of death and expected payout. For the group with family history (20% of 1,000 men), the probability is 1/50, and for the group without (80% of 1,000 men), it's 1/200. Thus, the premiums would be:
Group with history: (1/50) * $100,000 = $2,000Group without history: (1/200) * $100,000 = $500An actuarially fair premium for the group as a whole requires weighted averaging:
Premium whole group = (20% * $2,000) + (80% * $500) = $400 + $400 = $800
If the company charges this combined premium, it faces adverse selection; higher-risk individuals are more likely to purchase insurance, driving costs up.
An ice-cream shop sold 2.87 gallons of rocky road ice cream yesterday. The shop sold 0.449 gallons of rocky road ice cream today. What was the total amount of Rocky Road ice cream sold yesterday and today? Enter your answer, as a decimal, in the box.
PLEASE HELP ME! 50 POINTS IF YOU GET IT RIGHT!!
Darren flipped a quarter 40 times. The quarter landed on heads 65% of the time. How many times did the quarter land on tails ?
A 14
B 26
C 35
D 65
In the problem · N = 1, N must be _____. the additive inverse of the multiplicative inverse of the additive identity the multiplicative identity NEXT
The value N as shown in the question must be the multiplicative identity.
Multiplicative identityThe term multiplicative identity refers to that with which a number is multiplied and the result remains that number. Multiplying a number by its multiplicative identity returns the same value.
Therefore, the the problem, we can see that the value N as shown in the question must be the multiplicative identity.
Learn more about multiplicative identity: https://brainly.com/question/514731
Answer: the multiplicative inverse of 3/4
Step-by-step explanation: its right :)
There are 60 sixth graders, 50 seventh graders, and 70 eighth graders at your school. Every student gets entered in a raffle. What is the probability that an eighth-grade student will win the raffle?
x + y = 21 3y + x = 19 Which value of x is part of a solution to this system of equations?
Final answer:
The value of x that is part of a solution to this system of equations is 22.
Explanation:
To find the value of x in the system of equations:
x + y = 213y + x = 19We can use the method of elimination or substitution. Let's use substitution for this example:
Solve the first equation for y: y = 21 - x.Substitute the expression for y into the second equation: 3(21 - x) + x = 19.Simplify and solve for x: 63 - 3x + x = 19.Combine like terms: 63 - 2x = 19.Subtract 63 from both sides: -2x = -44.Divide by -2: x = 22.Thus, the value of x that is part of a solution to this system of equations is 22.
12 is 0.3% of what number?
Answer:
4,000
Step-by-step explanation:
A jar contains 3 red, 4 blue, and 2 white marbles. What is the probability that a marble drawn at random is not red?
Answer:
Probability that a marble drawn at random is not red = [tex]\frac{2}{3}[/tex].
Step-by-step explanation:
Given : A jar contains 3 red, 4 blue, and 2 white marbles.
To find : What is the probability that a marble drawn at random is not red.
Solution : We have given that
Red marbles = 3.
White marbles = 2.
Blue marbles = 4
Total marbles = 9
Marbles that are not red = white + blue =2+4 = 6.
Probability that a marble drawn at random is not red = [tex]\frac{Number\ of\ marbles\ not\ red}{Total\ that\ number\ of\ marbles}[/tex].
Probability that a marble drawn at random is not red = [tex]\frac{6}{9}[/tex].
Probability that a marble drawn at random is not red = [tex]\frac{2}{3}[/tex].
Therefore, Probability that a marble drawn at random is not red = [tex]\frac{2}{3}[/tex].
A gift bag is shaped like a rectangular prism and has a volume of 1152 cubic inches. The width of the bag is w, the length is 2w+4, and the height of the bag is 18-w (which is greater than the width). What are the dimensions of the bag?
Final answer:
In this high school math question, you will solve for the dimensions of a gift bag shaped like a rectangular prism using the given volume and expressions for width, length, and height.
Explanation:
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, the volume of the gift bag is 1152 cubic inches, so we have 1152 = w(2w+4)(18-w).
Solving this equation leads to w = 8, which means the width is 8 inches, length is 20 inches, and height is 10 inches.
Therefore, the dimensions of the gift bag are 8 inches width, 20 inches length, and 10 inches height.
Simplfy the expression: (x - 9)^2
If you see these clouds in the sky, which type of weather might you expect?
(Points : 3)
fog
no precipitation
heavy rain or snow
thunderstorms
At school athletic events you can buy 3 drinks and 2 hot dogs for $4.80 or you can buy 1 drink and 1 hot dog for $2.00. How much does 1 hot dog cost?
The sequence an= 27(1/3)^n-1 is graphed below. find the average rate of change between n=2 and n=4
A. - 1/4
B. 1/4
C. -4
D. 4
What is the simplest form of this binomial expression?
a4 − b4
Answer:
[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]
Step-by-step explanation:
The given expression is
[tex]a^{4}-b^{4}[/tex]
This expression is the difference of two perfect squares, and their square roots are
[tex]\sqrt{a^{4}} =a^{2}\\ \sqrt{b^{4}} =b^{2}[/tex]
Now, the difference of two perfect squares can be factored as
[tex]x^{2} -y^{2}=(x+y)(x-y)[/tex]
So, if we apply this rule, the result would be
[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]
Therefore, the simplest form of the binomial expression is
[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]
Answer and work in images
Is this right???? Can someone please help?
How to write a fraction with a numerator of 12 and a denominator of 13
SHIFT 2: 18 25 56 42 29 38 54 47 35 30. SHIFT 2: 23 19 50 49 67 34 30 59 40 33. SHIFT 3: 19 22 24 40 45 29 33 29 39 59. SHIFT 4: 21 23 25 40 35 19 70 40 22 23. The summary statistics for all of the workers at a steel factory are shown. Four sample groups were taken from each of the four shifts. For which sample group is the mean closest to the population mean?
Find the area of the figure.
There are 18 girls and 12 boys in class. What is the probability that a new kid in senior class will be a boy?
Cylinder a has a radius of 6 cm. Cylinder b has the same height and a radius half as long as cylinder a. What fraction of the volume of cylinder a is the volume of cylinder b what fraction of the volume of cylinder is the volume of cylinder? Explain.
Answer:
the answer is 1/4
Step-by-step explanation:
The area of a rectangular television screen is 3456 in^2. The width of that screen is 24 inches longer than the length. What is a quadratic equation the represents the area of the screen? What are the dimensions of the screen?
Final Answer:
Quadratic equation: [tex]\( x^2 + 24x - 3456 = 0 \)[/tex]
Dimensions: Length = 48 inches, Width = 72 inches
Explanation:
To find the quadratic equation representing the area of the screen, we first need to express the area as a product of its length (L) and width (W). Given that the width is 24 inches longer than the length, we can represent the width as [tex]\( L + 24 \)[/tex]. Thus, the equation becomes [tex]\( L \times (L + 24) = 3456 \)[/tex], which simplifies to the quadratic equation [tex]\( x^2 + 24x - 3456 = 0 \)[/tex], where x represents the length of the screen. Solving this equation yields the length x as 48 inches. Substituting this value back into [tex]\( L + 24 \)[/tex] gives the width as 72 inches. Therefore, the dimensions of the screen are 48 inches by 72 inches.
What is the area of the composite figure whose vertices have the following coordinates?
(−4, 3) , (2, 3) , (4, −1) , (0, −3) , (−2, −1)
Answer:
30 square units
Step-by-step explanation:
There are several ways to determine the area of the figure from its coordinates. A straightforward method is to plot the coordinates on a graph and decompose the resulting figure into simple shapes whose area formulas are known
Area from simpler shapesA plot reveals the figure to be a parallelogram with a base length 6 and a height of 4, together with a triangle of base 6 and height 2.
The area of the parallelogram is given by the formula ...
A = bh
The area of the triangle is given by the formula ...
A = 1/2bh
In each case, 'b' represents the base of the figure, and 'h' represents its height.
Parallelogram area
A = bh = (6)(4) = 24
Triangle area
A = 1/2bh = 1/2(6)(2) = 6
Total area
The composite area will be the sum of the parallelogram and triangle areas:
A = 24 +6 = 30 . . . . square units
The area of the composite figure is 30 square units.
__
Area from coordinatesThe area can also be figured directly from the coordinates. The formula for that can be written ...
[tex]\displaystyle A=\dfrac{1}{2}\left|\sum_{k=1}^n (x_k(y_{k+1}-y_{k-1}))\right|\qquad\text{where $y_0=y_n$ and $y_{n+1}=y_1$}[/tex]
Using this formula, we find the area to be ...
A = 1/2|(-4(3-(-1)) +2(-1-3) +4(-3-3) +0(-1-(-1)) -2(3-(-3))|
= 1/2|-16 -8 -24 +0 -12| = 1/2|-60| = 30
The area of the figure is 30 square units.