Old monthly payment = $966
New monthly payment = $605.10
Percent increase (to nearest tenth) = -37.3%
Given that,
Jim Tree bought a home with a 10% adjustable rate mortgage for 20 years.
He paid $9.66 monthly per thousand on his original loan.
At the end of 2 years, he owes the bank $55,000.
Interest rates have risen to 12%, and the bank will not renew the mortgage at this rate.
Jim can either pay the bank $55,000 or renew the mortgage at the higher interest rate.
Jim decides to renew and will now pay $11.02 monthly per thousand on his loan.
For comparison purposes, the small amount of principal that has been paid during the 2 years can be ignored.
Based on the information provided, Jim's old monthly payment can be calculated as follows:
Calculate Jim's original loan amount. We know that he paid $9.66 monthly per thousand on his original loan,
So if we divide his monthly payment by 1000,
We get his monthly interest rate:
$9.66 ÷ 1000 = 0.00966
Use the loan formula to calculate Jim's original loan amount:
Loan amount = Payment amount ÷ (Interest rate x (1 + Interest rate[tex])^N[/tex]- 1)
Where N is the number of payment.
Using this formula, and plugging in Jim's numbers, we get:
Loan amount = $9.66 ÷ (0.00966 x [tex](1 + 0.00966)^{240}[/tex] - 1)
= $100,000
Now that we know Jim's original loan amount, we can calculate his old monthly payment:
Old monthly payment = Loan amount x Payment amount per thousand
= $100,000 x $9.66
= $966
Therefore, Jim's old monthly payment was $966.
To calculate the new monthly payment and the percent increase,
We can follow these steps:
First, we need to calculate Jim's new loan amount.
We know that he owes the bank $55,000 after 2 years,
So we can use this amount as his new loan amount:
New loan amount = $55,000
Calculate Jim's new monthly interest rate.
We know that the interest rate has increased from 10% to 12%,
So we can calculate the new monthly interest rate as follows:
New monthly interest rate = 12% ÷ 12
= 0.01
Use the loan formula again to calculate Jim's new monthly payment:
New monthly payment = Loan amount x Payment amount per thousand
= $55,000 x $11.02
= $605.10
Therefore, Jim's new monthly payment is $605.10.
To calculate the percent increase,
we can use the following formula:
Percent increase = ((New value - Old value) ÷ Old value) x 100%
Plugging in Jim's numbers, we get:
Percent increase = ((605.10 - 966) ÷ 966) x 100% = -37.3%
Therefore, the percent increase (to the nearest tenth) is -37.3%.
However, note that this is a negative value, which means that Jim's new monthly payment is actually lower than his old monthly payment.
This is likely due to the fact that the loan amount has decreased significantly since Jim has already paid off a portion of the loan during the first 2 years.
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Final Answer:
Old monthly payment = $531.30
New monthly payment = $605.10
Percent increase in monthly payment (to the nearest tenth) = 13.9%
Explanation:
Let's calculate each part step by step.
Firstly, we will calculate the old monthly payment. Jim was paying at a rate of $9.66 monthly per thousand dollars of the original loan. We'll first determine how many thousands of dollars Jim owed at the beginning:
1. Old Monthly Payment:
Since he owes $55,000 at the end of 2 years and hasn't paid much towards the principal, we assume that the original loan amount was approximately $55,000.
Now, if he paid $9.66 per thousand dollars of the loan, we will calculate the monthly payment with the following steps:
- Divide the loan amount by 1,000 to find out how many "units" of $9.66 he would have to pay.
- Multiply the number of units by $9.66 to find the monthly payment.
Doing the calculations:
[tex]\( \frac{55,000}{1,000} = 55 \) units. \\\\\( 55 \text{ units} \times $9.66 = 55 \times 9.66 = $531.30 \).[/tex]
So, the old monthly payment was $531.30.
2. New Monthly Payment:
Now that the interest rate has increased to 12%, Jim will be paying at a rate of $11.02 monthly per thousand dollars.
Using the same method as above:
- Divide the loan amount by 1,000 to get the number of units.
- Multiply the number of units by $11.02 to find the new monthly payment.
Calculations:
[tex]\( \frac{55,000}{1,000} = 55 \) units.\\\\\( 55 \text{ units} \times $11.02 = 55 \times 11.02 = $605.10 \).[/tex]
So, the new monthly payment is $605.10.
3. Percent Increase in Monthly Payment:
To find the percent increase, we'll use the formula:
[tex]\[ \text{Percent Increase} = \left( \frac{\text{New Payment} - \text{Old Payment}}{\text{Old Payment}} \right) \times 100 \][/tex]
Performing the calculation:
[tex]\[ \text{Percent Increase} = \left( \frac{605.10 - 531.30}{531.30} \right) \times 100 \\\\\[ \text{Percent Increase} = \left( \frac{73.80}{531.30} \right) \times 100 \\\\\[ \text{Percent Increase} = 0.1388 \times 100 \\\\\[ \text{Percent Increase} = 13.88\% \][/tex]
To find the nearest tenth, we'll round the percent increase to one decimal place:
13.88% rounded to the nearest tenth is 13.9%.
Now, we can write down the final answers:
Old monthly payment = $531.30
New monthly payment = $605.10
Percent increase in monthly payment (to the nearest tenth) = 13.9%
Find the area of this polygon. Answer choices: A 41 square units
B 44 square units
C 52 square units
D 56 square units
Answer:
A
Step-by-step explanation:
Answer:
41 square units
Step-by-step explanation:
It would be easier to split this shape up into a square and a triangle at the y=5 line.
The area of the square would be 16 and the area of the triangle(1/2 base x height) would be 25. 16 + 25=41
Which sample size of a population of 200 is most likely to give a reliable conclusion?
Therefore, the sample size of a population of 200 is most likely to give a reliable conclusion is 80.
Answer:
80
Step-by-step explanation:
y = |x| translated one unit upward
Answer:
y = |x| + 1
Step-by-step explanation:
Answer:
y = |x| + 1
Step-by-step explanation:
Think about it first just in your head: if we want to translate up, that means every input (x) needs to be increased by one. The way to do this is by adding 1 outside of the absolute value sign!
You can also graph it online or on your calculator if you're confused!
The bedroom is 13ft. by 10ft. Determine the perimeter and area
Perimeter formula: 2b + 2h
Area formula: b * h
Perimeter:
2(13) + 2(10)
26 + 20
46
Area:
13 * 10
130
The perimeter is 46ft.²
The area is 130ft.²
Best of Luck!
In mathematics, the perimeter of the 13ft by 10ft bedroom would be 46ft and the area would be 130 square feet.
Explanation:The perimeter of a rectangle (which a bedroom is 13ft. by 10ft. mostly is) can be determined by adding up all the sides. So, the formula for a rectangle is: Perimeter = 2(length + width). Given that your length is 13ft and width is 10ft, the calculation would be Perimeter = 2(13ft + 10ft), resulting in a perimeter of 46ft.
The area of a rectangle is calculated by multiplying the length by the width. In this case: Area = length * width, therefore Area = 13ft. * 10ft., resulting in an area of 130 square feet.
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A \greenD{12\,\text{cm} \times 2\,\text{cm}}12cm×2cmstart color #1fab54, 12, start text, c, m, end text, times, 2, start text, c, m, end text, end color #1fab54 rectangle sits inside a circle with radius of \blueD{8\,\text{cm}}8cmstart color #11accd, 8, start text, c, m, end text, end color #11accd.
What is the area of the shaded region?
Answer:
[tex]177cm^2[/tex]
Step-by-step explanation:
Area of the Shaded region = Area of the Circle - Area of the Rectangle
[tex]=\pi r^2 -(LXB)\\r=8cm, L=12cm, B=2cm\\$Area of the Shaded region$ =[\frac{22}{7}X8^2]-[12X2] \\=201.14-24\\=177.14cm^2\\\approx 177cm^2[/tex]
Hope I was able to help you?
Answer:
the answer is 177.06 cm^2
Step-by-step explanation:
i just did it
Find the domain of the rational function 9x/(x+5)(x+3)
Answer:
the domain is : D = ]-∞ , -5[ U ]-5 , -3[ U ]-3 , +∞[
Step-by-step explanation:
hello :
f(x) = 9x/(x+5)(x+3)
f exist for : (x+5)(x+3) ≠ 0
(x+5)(x+3)=0
x+5=0 or x+3=0 means : x= - 5 or x= -3
the domain is : D = ]-∞ , -5[ U ]-5 , -3[ U ]-3 , +∞[
What’s does X-3 times X+5 equal
Answer:
x² + 2x - 15
Step-by-step explanation:
Given
(x - 3)(x + 5)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x + 5) - 3(x + 5) ← distribute both parenthesis
= x² + 5x - 3x - 15 ← collect like terms
= x² + 2x - 15
=
What is the relationship between two concentric circles with congruent radii?
Answer: Search Results
Featured snippet from the web
Congruent circles have congruent radii the plural of radius. Concentric circles have the same center. A central angle has a vertex on the center and endpoints on the circle. given point
What is the solution of the following system?
y=-x+2
y=-4x – 1
Your answer
Answer:
y = 3
x = -1
Step-by-step explanation:
The idea to start the problem is that we need to cancel x in one equation to find y first, therefore:
y = -x + 2 (let's multiply this entire equation by -4)
y = -4x - 1
We then have .:
- 4y = 4x - 8
y = -4x - 1 (now we sum both equations)
.:
- 3y = -9 (isolate y)
y = -9 / -3
y = 3 (good we have y!)
Now come back to one of the equations, substitute y to find your x!
Substituting on the first equation we have:
3 = -x +2 (isolate x)
3 - 2 = -x
1 = -x (multiply everything by -1)
x = -1
I hope it helps :)
Circle Q has a circumference of approximately 50 centimeters.What is the approximate length of the diameter, d? Use 3.14 for . Round to the nearest tenth of a centimeter.
Answer:
15.92
Step-by-step explanation:
50 ÷ 3.14 = 15.92
Which linear function has a y-intercept at –3?
Answer:
Cant answer
Step-by-step explanation:
Depending on the option choices and without seeing the option choices I can give you an idea of how to solve this.
Using y=mx+b we can find the y intercept by knowing that B is the value of the y Intercept
Answer:
(0,-3)
Step-by-step explanation:
Find the m the slope (Y-y)/(X-x) using the two points given. Step 2 - Find b using slope- intercept y = mx + b and 1 of the points given.
Write an expression for the sequence of operations described below.
divide w by 3, then subtract 10 from the result
Do not simplify any part of the expression.
Answer:
(w/3)-10
Hope this helps!
w/3 - 10 is an expression for the above-described series of operations.
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given, divide w by 3, then subtract 10 from the result Do not simplify any part of the expression.
We need to Create an expression for the above sequence
divide w by 3
=> w/3
then subtract 10
=> w/3 - 10
Since it's written in the problem that does not simplify hence, we would simplify this equation further.
Therefore, an expression for the sequence of operations described above is w/3 - 10
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PLZ HELP! WORTH EXTRA POINTS!! PYTHAGREOM THEROEM WITH 3D SHAPES
Answer:
16 units
Step-by-step explanation:
Using the Pythagorean theorem, we can find 1/2 the length of b. We will call it x
15^2 + (x)^2 = 17^2
225 + x^2= 289
Subtract 225 from each side
x^2 = 289-225
x^2 =64
Take the square root of each side
sqrt(x^2) = sqrt(64)
x =8
This is one half the length of b
b= 2*8
b = 16
Answer:
16
Step-by-step explanation:
17² = 15² + (b/2)²
64 = (b/2)²
b/2 = 8
b = 16
If Ezra works less than or equal to 50 hours doing lawn care, he must spend at least __ hours walking dogs.
Final answer:
If Ezra works less than or equal to 50 hours doing lawn care, he must spend at least [answer] hours walking dogs.
Explanation:
To determine the minimum number of hours Ezra must spend walking dogs when he works less than or equal to 50 hours doing lawn care, we need to refer to the given information and apply it to the situation
According to the exercise, Louis requires one hour to cut a typical lawn, while Carrie Anne needs one and one-half hours. Therefore, Louis is more efficient at cutting grass. Carrie Anne, on the other hand, can wash a car in half an hour, while Louis requires three-quarters of an hour. So, Carrie Anne is more efficient at cleaning cars.
If they each specialize in the task they are most efficient at, Louis should cut the grass, and Carrie Anne should wash cars. This way, they can maximize their output in a given amount of time.
Now, if they each work a twelve-hour day, we can calculate how many lawns they can cut and how many cars they can wash based on their efficiency. Louis can cut 12 lawns (since he requires 1 hour per lawn), and Carrie Anne can wash 24 cars (since she can wash a car in 0.5 hours).
Therefore, if they specialize in their most efficient tasks, they can cut 12 lawns and wash 24 cars in a twelve-hour day.
Answer:
IT IS 35
Step-by-step explanation:
What is the scale factor ASAP
and why
Answer:
The SF is 2/3
Step-by-step explanation:
You can find this out by creating a ratio between the points and it's image. The one with the apostrophe is the image, and the bigger one is the pre-image.
Nancy goes out to lunch with. Jason and tim the total bill came to 27 dollars they decided to split the bill how much will each person pay?
Answer:
$13.5
Step-by-step explanation:
27/2 = 13.5
Grace had 4 3/8 yards of elastic. She used 1 2/3 yards of the elastic to make bracelets for her friends. How many yards of elastic does she have now?
6 1/24 yards
3 7/24 yards
2 17/24 yards
3 17/24 yards
Answer:
Exact form: 65/24
Decimal form: 2.7083
Mixed number form: 2 17/24
Step-by-step explanation:
4 3/8 - 1 2/3 = 2 17/24
how do you select a month of the year at random what is the probability that the month ends with the ER
Answer:
4/12 or 1/3
Step-by-step explanation:
Answer:
1:3 or 1/3
Step-by-step explanation:
September, October, November, December
4 moths out of twelve
4/12 reduces to 1/3
The answer could be written 1/3 or 1:3.
-1/2x>4 solve for x
Answer:
X<-8
Step-by-step explanation:
-1/2x>4
Multiple both sides by -2
-2(-1/2)x<-2(4)
Multiple even numbers of negative terms
2(1/2)x<-2(4)
Cancel out the 2
(2 this is out)(1/(2 this is out))x<-2(4)
x<-2×4
Multiple
x<-8
3x-4y=1 and x=2y+1 using substitution
Answer:
x =-1
y =-1
Step-by-step explanation:
to solve this system of equation, using substiution method
3x-4y=1 ........................ equation 1
x=2y+1 ............................ equation 2
subbstitute for x into equation 1
3x-4y=1 ........................ equation 1
3(2y + 1) - 4y = 1
6y + 3 -4y = 1
2y + 3 = 1
collect the like terms
2y = 1- 3
2y= -2
divide both sides by the coefficient of y which is y
2y/2 = -2/2
y = -1
put the value of y =-1 into equation 2
x=2y+1 ............................ equation 2
x = 2(-1) + 1
x = -2 + 1
x = -1
therefore x =-1 y = -1
Re-write the quadratic function below in Standard Form
y = -7(x + 9) (x - 1)
Answer:
-7x squared -56x+63.
Step-by-step explanation:
Hope this helps!
Which point on the number line represent 42?
A.P
B.Q
C.R
D.S
Answer:
Q
Step-by-step explanation:
because 42 square rooted is between 6 and 7.
What is the radius of the circle given by the equation below?
x2 + 12x + y2 - 12y = -56
A. 2
B. 16
C. 4
D. 8
Answer:
C
Step-by-step explanation:
First, you gotta complete the square!
x^2+12x+36 = (x+6)^2
y^2-12y+36 = (y-6)^2
So, we have (x+12)^2 + (y-6)^2 = -56 + 36 + 36
The right side of the equation is the radius^2.
Simplify:
-56 + 36 + 36 = 16
The square root of 16 is 4, so the answer is C!
What is the length of Line A B? On a coordinate plane, point A is (negative 4, 3), point B is (2, 3), and point C is (2, negative 1). 4 units 5 units 6 units 7 units
Answer:
6 units
Step-by-step explanation:
Answer:
6 units
Step-by-step explanation:
Students in middle school and high school were surveyed about whether they have taken the SAT. Some of the survey results are listed here.
37% of middle school students have taken the SAT.
4% of high school students have not taken the SAT.
This information is shown in the two-way frequency table below. Drag numbers into the empty spaces to complete the table.
Answer:
Step-by-step explanation:k so high school total should be 100%
middle school not taken SAT should be 63%
high school have taken SAT should be 96%
basically just use your basic math. Turn the problem around and take the total(100%) and subtract what number you already know. So like This:
100-37=63
100-4=96
The subject of this question is SAT and it is related to middle school and high school. The answer provides an explanation of the survey results regarding students taking the SAT.
Explanation:The subject of this question is SAT. The grade level of this question is Middle School, High School.
The table provided shows the survey results of whether middle school students and high school students have taken the SAT. From the information given, we can determine the missing values in the table:
Middle School Students Taken SAT = 37%
High School Students Not Taken SAT = 4%
*Please note that the table was not provided with the question, so we are unable to fill in the missing values.
If you flip a coin and roll a six sided die what is the probability that you flip a heads and roll a five?
Answer:
you have a 50-50% of landing heads and a 5 out 6 % chance of rolling a 5
Step-by-step explanation:
Answer: 1/12
Step-by-step explanation:
What is the amount of sales tax on a $48 backpack if the sales tax rate is 6%?
Answer: 2.88
Step-by-step explanation:
48 x 0.06 = 2.88 and thats how much tax you will pay!!
What does this equal 3 7/12 + 4 9/12=
Hope this will help u...
A group of students were surveyed about their interest in a new International Studies program. Interest was measured in terms of high, medium, or low. 30 students responded high interest; 50 students responded medium interest; 20 students responded low interest. What is the relative frequency of students with high interest? A) 30% B) 50% C) 40% D) Cannot be de
Answer:
Relative frequency is the number of times an envent has occured.
When finding out the number of students with high interest you would take 30/100 because there was 30 students with high frequency and 100 students all together.
30/100=30%
A)30%
Hope this helps ;)
The relative frequency of students with high interest in the new International Studies program is 30%. This is calculated by dividing the number of high interest responses (30) by the total number of responses (100), and multiplying the result by 100.
Explanation:The question asks us to calculate the relative frequency of students with high interest in the new International Studies program. To do this, we divide the number of students with high interest by the total number of students surveyed.
The total number of students polled is 30 (high interest) + 50 (medium interest) + 20 (low interest), which equals 100 students. So, to calculate the relative frequency for students with high interest, we divide the number of students with high interest (30) by the total number of students surveyed (100).
The calculation is as follows: (30 / 100) * 100 = 30%
Therefore, the relative frequency of students with high interest is 30%, which corresponds to option A in your multiple choice question.
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A block is set in motion hanging from a spring and oscillates about its resting position
x = 0
according to the function
x = 0.6sin(2t)+0.4cos(2t),
where x is in centimeters and t is in seconds. For what values of t in the interval [0,3] is the block at its resting position
x =0?
Answer:
t = 1.277 sec and t = 2.848 sec
Step-by-step explanation:
This problem is much more easily done by graphing it than by computing it using algebra.
The values of t we're looking for are the ones that make x = 0, so we want the solutions of [tex]0.6sin(2t)+0.4cos(2t)=0[/tex] on the interval [0, 3].
According to the graph, this is true when t = 1.277 seconds and t = 2.848 seconds.
Answer:
t = 1.28, 2.85
Step-by-step explanation:
x = 0.6sin(2t)+0.4cos(2t)
x = 0, so
0.6sin(2t)+0.4cos(2t) = 0
0.6sin(2t) = -0.4cos(2t)
Convert into tan(2t) by dividing both sides by 0.6cos(2t):
tan(2t) = -0.4/0.6
tan(2t) =-2/3
Since t lies in [0,3] ,
2t lies in [0,6]
tan(2t) =-2/3
Basic angle:
0.5880026035
Tan is negative is second and fourth quadrants
2t = 2.553590005, 5.695182704
t = 1.276795025, 2.847591352