To calculate Frederick's approximate savings if he paid off the loan early, subtract the total amount he would pay if the loan continued for the full term from the original loan amount. The monthly payment amount can be calculated using the compound interest formula. By multiplying the monthly payment by the number of payments, you can find the total amount paid over 20 years. Subtracting this from the original loan amount gives you the approximate savings.
Explanation:To calculate the approximate amount Frederick would save if he paid off the loan early, we need to find the total amount he would pay if he continued making monthly payments for the full 20 years and subtract the total amount he would pay if he paid off the loan early.
1. First, find the monthly interest rate by dividing the annual interest rate by 12:
i = 0.022 / 12 = 0.00183
2. Next, calculate the monthly payment using the compound interest formula:
P = (r * PV) / (1 - (1 + r)^(-n))
Where P is the monthly payment, r is the monthly interest rate, PV is the loan amount, and n is the number of monthly payments.
3. Substitute the values into the formula:
P = (0.00183 * $70,000) / (1 - (1 + 0.00183)^(-240))
4. Solve for P to find the monthly payment amount:
P ~ $520.63
5. To find the total amount paid over 20 years, multiply the monthly payment by the number of payments:
Total amount paid = $520.63 * 240 = $124,950.98
6. To find the approximate amount saved if the loan is paid off early, subtract the total amount paid from the original loan amount:
Approximate savings = $70,000 - $124,950.98 = -$54,950.98
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Final answer:
Frederick would save approximately $34,692.80 if he paid off the loan early.
Explanation:
To calculate the amount Frederick would save if he paid off the loan early, we need to determine the total cost of the loan and compare it to the amount he would pay if he paid it off in a shorter time period.
First, we need to calculate the monthly payment using the formula:
Monthly Payment = Loan Amount * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Total Number of Payments)))
Substituting the values, we have:
Loan Amount = $70,000
Monthly Interest Rate = 2.2% / 12 = 0.1833%
Total Number of Payments = 20 * 12 = 240
Plugging the values into the formula, we get:
Monthly Payment = $70,000 * (0.1833% / (1 - (1 + 0.1833%)^(-240)))
Calculating this equation gives us a monthly payment of approximately $436.22.
Next, we calculate the total cost of the loan by multiplying the monthly payment by the total number of payments:
Total Cost = Monthly Payment * Total Number of Payments
Plugging in the values, we get:
Total Cost = $436.22 * 240
Calculating this equation gives us a total cost of approximately $104,692.80.
If Frederick paid off the loan early, he would save the difference between the total cost and the original loan amount, which is $104,692.80 - $70,000 = $34,692.80.
What is 26.99 round to the nearest tenth
To round 26.99 to the nearest tenth, we increase the tenths place by 1 because the hundredths place is 9, resulting in 27.0.
When rounding 26.99 to the nearest tenth, we need to look at the hundredths place, which is 9. Since 9 is greater than 5, we round up the digit in the tenths place by 1. Therefore, the number rounded to the nearest tenth is 27.0.
Describe and correct the error made in solving the system of equations by elimination
The error that was made is that the constant term in the second equation was not multiplied by 5.
How to solve these system of linear equations?In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method and Addition Method.
Based on the information provided, we have the following system of linear equations:
5x + 3y - z = 15 .........equation 1.
-x + 2y + 3z = 10 .........equation 2.
By multiplying the second equation by 5, we have the following:
(-x + 2y + 3z = 10) × 5 = -5x + 10y + 15z = 50 .........equation 3.
By adding equation 1 and equation 3, we have the following:
5x + 3y - z = 15
-5x + 10y + 15z = 50
13y + 14z = 65
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y = 4
y = 1/4 x +2
What is the x coordinate of the solution to the system of the linear equations?
A. 0
B. 2
C. 4
D. 8
Suppose a and b are integers. How many solutions are there to the equation ab = 2a + 3b?
PRE-CAL/CAL MASTER NEEDED
f ( 2x − 1 ) = 4x^2 − 10x + 6
from f(x)=x^2-3x+2, h(x)=2x-1, f(h(x))
How is this: f ( 2x − 1 ) = 4x^2 − 10x + 6 derived from ^
The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 10 fl oz per hour. How fast was the pipe leaking in gallons per day?
Answer:
The pipe is leaking at the rate of 1.875 gallons of water per day.
Step-by-step explanation:
In this question we will find the leakage per day first, then convert it into gallons.
The janitor discovered a leak, leaking with a rate = 10 oz per hour
And we know that there are 24 hours in a day therefore, pipe leaking per day will be = 24×10 = 240 oz.
Since 1 oz = 0.0078125 gallons
Therefore, 240 oz = 240×0.0078125
= 1.875 gallons
The pipe is leaking at the rate of 1.875 gallons of water per day.
Ms. Sims is putting away 22 books. She can put them on the table in stacks of 10 or as single books. What are the different ways Ms. Sims can put away the books?
Answer:
1)[tex]10+10+1+1=22[/tex]
2)[tex]10+1+1+1+1+1+1+1+1+1+1+1+1=22[/tex]
Step-by-step explanation:
Mrs. Sims has to put 22 books.
She can either put them in stacks of 10 or arrange them as single book(single stack).
There could be two ways in which she could arrange the books.
First way:
She could arrange the books in two stacks of 10 books ([tex]2\times10=20[/tex] and the remaining two books can be arranged as single books.
So, the arrangement is [tex]10+10+1+1=22[/tex]
Second way:
She could arrange books in one stack of 10 books and and remaining twelve books can be arranged as single books.
So, the arrangement is [tex]10+1+1+1+1+1+1+1+1+1+1+1+1=22[/tex]
What is the e-file rejection error for an Invalid bank account or routing transit numbers?
Answer;
The Error code "0019".
Explanation;
-The e-file rejection error for an invalid bank account or routing transit numbers is error code "0019".
-This error code may be caused by a variety of reasons and is present in tax accounting software, where an e-file sent to the IRS is rejected, hence the error name. An incomplete installation might be one of the several reasons behind an e-file rejection error.
How long does it take $450 to double at simple interest rate of 100%
Final answer:
It will take 1 year for $450 to double at a simple interest rate of 100%, as the simple interest formula shows that the interest equals the principal when the rate is 100% and time is one year.
Explanation:
To calculate how long it takes for $450 to double at a simple interest rate of 100%, we can use the formula for simple interest: Interest = Principal × Rate × Time. Since the goal is to double the principal, the interest earned should be equal to the principal of $450.
The simple interest formula in this shape becomes:
$450 = $450 × 1 × Time
When we simplify this, we find that Time equals 1.
Therefore, it will take 1 year for $450 to double at a simple interest rate of 100%.
Corey needs 24 boards that ate 47 1/ 2 inches long. How many feet of boards should he buy. Explain
how do i use parentheses to rewrite 16 - 4 × 3 + 7 so that it equals 120?
(16-4) x (3+7) =120
when we subtract 16 and 4 you get 12.
When we add 3+7 you get 10.
After multiplying them together we get 120.
What are parentheses those called?
parentheses
Parentheses are a pair of punctuation marks that might be most customarily used to feature extra nonessential information or an aside to a sentence. Parentheses resemble two curved vertical lines: ( ). An unmarried one of these punctuation marks is called a parenthesis.
How do you operate parentheses?Use parentheses to surround additional or supplemental data that clarifies or illustrates a point. Use parentheses to offer a digression or afterthought.Use parentheses to surround numbers or letters introducing objects in a list or outline.Learn more about parentheses here: https://brainly.com/question/1473593
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Multiply 16.852 × 0.86
A home is to be built on a 56 foot 9 inch wide lot. The house is 5 feet 5 inches from the side of the lot and is 34 feet 10 inches wide. How far is the house from the other side of the lot?
Answer:
132
123
Step-by-step explanation:
A produce store sold 63 red apples. If the ratio of red apples to green apples sold was 7:2, what is the combined amount of red and green apples sold?
The total number of apples sold if, A produce store sold 63 red apples, The ratio of red apples to green apples sold was 7:2, which is 81.
What is the ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.
Given:
A produce store sold 63 red apples,
The ratio of red apples to green apples sold was 7:2,
Assume the total number of apples sold is x then,
Total number of apple sold = 7x + 2x
But the number of red apples sold is given so,
7x = 63
x = 63 / 7
x = 9
Put the value of x in the above equation,
Total number of apple sold = 7 × 9 + 2 × 9
Total number of apple sold = 63 + 18
Total number of apples sold = 81
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Solve the equation, and check the answer
5g+4(-5+3)=1-g
Tamara’s dosage of medication has recently decreased 20 milligrams per day. What is the total decrease in Tamara’s medication at the end of the week? Show your work.
Type answer here
use the model to write an equivalent fraction 3 over 4
6/8 , 9/12 are the equivalent fraction 3 over 4
What is Fraction?A fraction represents a part of a whole.
The given fraction is 3/4.
In the given fraction the numerator is three and denominator is four.
We need to find the equivalent fractions of 3/4.
Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value.
Let us multiply with same number in numerator and denominator to find the equivalent fractions.
3/4×2/2=6/8
3/4×3/3=9/12
Hence, 6/8 , 9/12 are the equivalent fraction 3 over 4
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Ok folks 4 questions and 50 points up for grabs for correct answers....Need quickly thanks!!!
1. 2*0.8 = 1.6 PQ = 1.6
2. arctan(14/12) = 49.4 degrees
3. 15 * cos(70) = 5.1 feet
4. x = 30 * cos(40) = 22.9813 = 23.0 miles
y = 30 *sin(40) = 19.2836 = 19.3 miles
Can you use the values in Pascal’s triangle to find the powers of 11? Explain.
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Yes!
Ultimately (it states) all numbers in existence can be extracted from Pascal's Triangle. Using his binomial formation of: (a + b)^0 = 1 , where y is the number you are using. and (a + b)^x is the equation you use to find the answer of that row... the usage of that row, and the formation of its components is how you find the powers of numbers in a given row...
You would be able to find each row of the Triangle, and by using the association of Multiplication, addition, distribution, and
If you look at the images below you will notice that to find a power of 11 at it's 6th power, you look at the 6th row of Pascal's Triangle... Although not completely relevant, I also added an image of using his Triangle to find the Powers of 2...
Remember, The images below are of only smaller versions of Pascal's Triangle, as his Triangle is of infinite size...
Yes, we can use the values in Pascal’s triangle to find the powers of 11
What is Pascal triangle?Pascal triangles contains coefficient of (x + 1)'s expanded form's terms.
For first row, we have:
Thus, 1 is the value in the first row of Pascal triangle.
(x + 1) = 1
The variable x has coefficient 1, and that 1 itself, so second row of Pascal triangle has 1 , 1 as values.
It states that all numbers in existence can be extracted from Pascal's Triangle.
Using his binomial formation;
(a + b)^0 = 1 , where y is the number
(a + b)^x is the equation that use to find the answer of that row. the usage of that row, and the formation of its components isto find the powers of numbers in a given row.
It would be able to find each row of the Triangle, and by using the association of Multiplication, addition, distribution.
Yes, we can use the values in Pascal’s triangle to find the powers of 11
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The tax rate as a percent, r, charged on an item can be determined using the formula – 1 = r, where c is the final cost of the item and p is the price of the item before tax. Louise rewrites the equation to solve for the final cost of the item: c = p(1 + ). What is the final cost of a $40 item after an 8% tax is applied?
Answer:$43.20
Step-by-step explanation:
Simplify and determine the coefficient of (-x)(3y)(-2x).
a.-4
b.1/3
c.1
d.4
well.. i just got the same problem.. With the same multiple choice.. I'm going to put one. I might update with my score on the test after i finish. (this is an old question that i thought i might answer with my guess)
Simplify. −2i ⋅ (−3i)
a.−6i
b. 6
c. −6
d. 6i
HURRY!
To simplify -2i * -3i, multiply -2 by -3 to get 6, then multiply i by i to get i². Because i² is equivalent to -1 in the complex number system, multiply 6 by -1 to get your answer, which is -6.
Explanation:When multiplying two complex numbers like −2i and (−3i), the 'i' terms get multiplied together separately to the numerical terms. This is due to the distributive property of multiplication.
So, if we apply the multiplication, we would have −2 multiplied by −3 which gives us 6. Then, i multiplied by i gives us i². The term i² is defined as -1 in the realm of complex numbers.
Putting these together we get 6 x -1, that results in −6.
Therefore, the simplified value of the expression is -6, which corresponds with option c.
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What is the value of digit 0 in 175,028
Answer:
its in the hundreads place but it has no value becuase its 0
Step-by-step explanation:
A ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 6 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth
The length of the ladder is 11.66 ft.
What is the Pythagoras theorem?The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
a² + b² = c²
Given that a ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 6 ft from the side of the house.
Let the length of the ladder be x
Therefore, using Pythagoras theorem
x² = 10² + 6²
x² = 100 + 36
x = [tex]\sqrt{136[/tex]
x = 11.66 ft
Hence, the length of the ladder is 11.66 ft.
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Evaluate the expression for the given value.
36 ÷ m when m = 9
A.
324
B.
45
C.
27
D.
4
A line with a slope of -2 crosses the y-axis at (0, 3). The equation of the line is
what us the average rate of change
the rate of change is -2 for every set shown in the chart on the right
so 6 to 7 would be -11 -2 = -13
7 to 8 would be -13-2 = -15
8 to 9 = -15-2 = -17
B is the answer
Water is flowing out of a conical funnel through its apex at a rate of 12 cubic inches per minute. If the tunnel is initially full, how long will it take for it to be one-third full? What is the height of the water level? Assume the radius to be 3 inches and the altitude of the cone to be 4 inches.
A child is to receive a dose of 0.5 teaspoon of cough medicine every 6 hours. If the bottle contains 24 doses, how many days will the medicine last?
He burj khalifa is 828,000,000 micrometers tall. how is this value written in scientific notation in the gizmo™?
To write this in scientific notation, we have to move the decimal place to the left. Moving the decimal place to the left indicate a positive movement, therefore the correct scientific notation in this case is:
8.28 x 10^8 micrometers