Prepare an amortization schedule for the first three months on a loan of $87000 at 6% for 20 years
Answers
First, we need to calculate the value of the monthly payments. We can use the general ordinary anuity formula:
[tex]PV=\text{PMT}\cdot\lbrack\frac{1-(1+i)^{-n}}{i}\rbrack[/tex]Where PV=$87000
n=20
i=0.06
Replace the given values and solve for PMT:
[tex]\begin{gathered} 87000=\text{PMT}\cdot\lbrack\frac{1-(1+0.06)^{-20}}{0.06}\rbrack \\ 87000=\text{PMT}\cdot\lbrack\frac{1-0.3118}{0.06}\rbrack \\ 87000=\text{PMT}\cdot\lbrack\frac{0.6882}{0.06}\rbrack \\ 87000=\text{PMT}\cdot11.4699 \\ \text{PMT}=\frac{87000}{11.4699} \\ \text{PMT}=7585.06 \end{gathered}[/tex]Now that you have the payment, you can construct the table of the amortization schedule with the know information:
To calculate the missing information, start by calculating the interest component of the payment (interest paid) by multiplying the periodic interest by the remaining principal.
The monthly interest is the yearly interest divided by 12, then:
[tex]MI=\frac{0.06}{12}=0.005[/tex]And the interest paid is then:
[tex]\begin{gathered} IP=MI\cdot\text{ Remaining principal} \\ IP=0.005\cdot87000\text{ (for the first payment)} \\ IP=435 \end{gathered}[/tex]Now, calculate the principal paid by subtracting the interest paid from the payment amount:
[tex]\text{ Principal paid=7585.06-435}=7150.06\text{ (first payment)}[/tex]Then, by putting the values on the amortization schedule:
The remaining principal is 87000-7150.06 (principal paid).
Now for the second payment, calculate the interest paid with the new remaining principal:
[tex]\begin{gathered} IP=0.005\cdot79849,94\text{ (for the second payment)} \\ IP=399,25 \end{gathered}[/tex]And the principal paid is:
[tex]\text{ Principal paid=7585.06-399.25}=7185.81\text{ (second payment)}[/tex]The remaining principal is:
[tex]RP=79849.94-7185.81=72664.13[/tex]Thus:
And for the third month, you apply the same calculations and the amortization schedule is:
Related Questions
Graph the line.y-1= 1/5 (x+4)
Answers
We are given the following equation:
[tex]y-1=\frac{1}{5}(x+4)[/tex]Using the distributive property:
[tex]y-1=\frac{1}{5}x+\frac{4}{5}[/tex]Adding 1 to both sides
[tex]y=\frac{1}{5}x+\frac{4}{5}+1[/tex]Solving the operations:
[tex]y=\frac{1}{5}x+\frac{9}{5}[/tex]To graph this line we need two points through which the line passes. The first point can be obtained by making x = 0:
[tex]\begin{gathered} y=\frac{1}{5}(0)+\frac{9}{5} \\ y=\frac{9}{5} \end{gathered}[/tex]Therefore, the first point is (0,9/5).
The second point can be obtained by making x = 1, we get:
[tex]\begin{gathered} y=\frac{1}{5}(1)+\frac{9}{5} \\ y=\frac{10}{5}=2 \end{gathered}[/tex]Therefore, the point is (1,2). Now we plot both points and join them with a line. The graph is:
what digit is in the
Answers
SOLUTION
Given the question in the image, the following are steps to solve the question.
Step 1: Write out the given function to be plotted on the graph.
[tex]x=6[/tex]Step 2: Plot the function on the graph. Please note that x=6 means that the line on the graph will pass through the point where x-axis is equal to 6. This can be better explained on the graph below.
The red line passing through x-axis at point 6 indicates x=6.
The graph below shows an office worker's annual salary:What are the domain and range of the function? Why are the x-values nonnegative?
Answers
Okay, here we have this:
Considering that the domain refers to the possible values of x that can be substituted in the correspondence rule of a function. We can see in the function that the domain is [0, +∞) (because there is an arrow that indicates that it continues to increase).
And as the range is the set of numbers that depend on the substitution (tabulation) of the values that "x" can take. We can see that the range is [5000, +∞).
And the number of years is non-negative because the years that elapse are always counted forward, that is, they begin to count from zero.
find the slope of the line. 5x-2y=7
Answers
Thus 5/2 is the slo
9 x+3=9 3x=9 3+x=9 x=9-3 x=9=3 < those are the answers
Answers
Based on the diagram of the figure, the equation is:
x + 3 = 9
I need help to simplify 3x (x² - x - 2) + 2x (3 - x) - 7x. I've tried to solve the problem three times and have gotten 2x² - 2x - 6, then, x² - 1x - 6, then, 3x³ - 5x² - 13x, I can't figure out what I'm doing wrong.
Answers
Given the initial expression,
[tex]3x(x^2-x-2)+2x(3-x)-7x[/tex]Simplify it as shown below
[tex]\begin{gathered} =3x*x^2-3x*x-3x*2+2x*3-2x*x-7x \\ =3x^3-3x^2-6x+6x-2x^2-7x \end{gathered}[/tex][tex]\begin{gathered} =3x^3-3x^2-2x^2-7x \\ =3x^3-5x^2-7x \end{gathered}[/tex]Thus, the answer is 3x^3-5x^2-7xSolve for X using cosine law along with with written explanation.
Answers
Given:
The two sides and angle of triangle are
[tex]\begin{gathered} a=19m \\ b=25m \\ \angle C=65\degree \end{gathered}[/tex]Required:
To find the value of X.
Explanation:
By cosine rule
[tex]\begin{gathered} X=\sqrt{a^2+b^2-2ab\cos C} \\ \\ =\sqrt{19^2+25^2-2\times19\times25\cos65} \\ \\ =24.17m \end{gathered}[/tex]Final Answer:
The value of X is
[tex]X=24.17m[/tex]I need help with my math
Answers
we have
8.13x10^5
convert to standard form
10^5=100,000
substitute
8.13x10^5=8.13*(100,000)=813,000
therefore
answer is
813,000Select ALL the expressions that have the same value as 9s
1. 9+s
2. 9*s
3. 3s + 6s
4. 3(3s)
5. s(5+4)
6. 3s * 3s
7. s+s+s+s+s+s+s+s+s2. 3s+2t=-4-6s-10t=-7What’s the value of s ?
Answers
ANSWER
2, 3, 4, 5, and 7 are the correct expressions that have the same values as 9s
STEP-BY-STEP EXPLANATION
Using Simultaneous equation
3s + 2t = -4 .............................................(1)
-6s - 10t = -7 .............................................(2)
multiply equation 1 by 2 and multiply equation 2 by 1:
equ 1 x 2: 6s + 4t = -8 ...............................(3)
equ 2 x 1: -6s -10t = -7 ................................(4)
Add equation 3 and 4 together
0s -6t = - 15
Divide through by -6:
[tex]\begin{gathered} t\text{ = }\frac{-15}{-6} \\ t\text{ = }\frac{5}{2} \end{gathered}[/tex]substitute the value of t into equation 1:
[tex]\begin{gathered} 3s\text{ + 2t = -4} \\ 3s\text{ + 2(}\frac{5}{2})\text{ = -4} \\ 3s\text{ + 5 = -4} \\ 3s\text{ = -4 -5} \\ 3s\text{ = -9 } \\ s\text{ = }\frac{-9}{3} \\ s\text{ = -3} \\ \end{gathered}[/tex]Now solving for the expression that has the same value as 9s:
Note: 9s = 9(-3) = -27
1. 9 + s = 9 - 3 = 6
2. 9 * s = 9 * -3 = -27
3. 3s + 6s = 3(-3) + 6(-3) = -9 -18 = -27
4. 3(3s) = 9s = 9(-3) = -27
5. s(5 + 4) = s(9) = -3(9) = -27
6. 3s * 3s = 3(-3) * 3(-3) = -9 * -9 = 81
7. s+s+s+s+s+s+s+s+s = -3-3-3-3-3-3-3-3-3 = -27
Hence, 2, 3, 4, 5, and 7 are the correct expressions that have the same values as 9s.
6.Subtraction Solve: 4t+5=k t=6
Answers
We have the following:
[tex]\begin{gathered} 4t+5=k \\ t=6 \end{gathered}[/tex]replacing and solving:
[tex]\begin{gathered} 4\cdot6+5=k \\ k=24+5 \\ k=29 \end{gathered}[/tex]The value of k is 29
I know the first part but having trouble on the second part
Answers
Take into account that the standard deviation of a probability distribution table is given by:
[tex]\sigma=\sqrt[\placeholder{⬚}]{\Sigma\left(x-\mu\right)^2P\left(x\right)}[/tex]where x is each element of the first column of the table, μ is the mean and P(x) is the corresponding values of P(x) for each value of x in the second column.
By replacing the values of the table you obtain:
[tex]\begin{gathered} \sigma=\sqrt[\placeholder{⬚}]{\left(0-3.79\right)^2\lparen0.04)+\left(1-3.79\right)^2\left(0.23\right)+\left(3-3.79\right)^2\left(0.35\right)+\left(6-3.79\right)^2\left(0.15\right)+\left(7-3.79\right)^2\left(0.23\right)} \\ \sigma=\sqrt[\placeholder{⬚}]{5.6859} \\ \sigma\approx2.38 \end{gathered}[/tex]Hence, the standard deviation of the given data is approximately 2.38
Which graph shows the transformation of the function f(x)=e^x where the function is translated four units to the right, vertically compressed by a factor of 1/3, and translated down five units then translated five units down?
Answers
The graph that shows the transformation of the function f(x) = e^x is option D.
Step - by - Step Explanation
What to find? The transformation of the function f(x)=e^x.
Given:
• f(x) = 4^x
,• Vertially compresses by a factor 1/3
,• Translated four units to the right.
,• Translated down five units.
Note that:
• If f(x) shifts up m- units, then we have f(x) + m.
,• If f(x) shifts down n-units then we have f(x) - n.
,• If f(x) shifts right p - units, then we have f(x - p).
,• If f(x) shifts left q - units, then we have f(x+q).
From the given question, f(x) is translated four units to the right., hence e^x becomes eˣ⁻⁴
f(x) is further compressed by a factor of 1/3, the function becomes 1/3 eˣ⁻⁴.
Finally, the function is translated down five units, hence, the function becomes:
[tex]f(x)=\frac{1}{3}e^{x-4}-5[/tex]The graph of the function after the translation is
What is the average value of -2/5, 7/10, 1/2, -1/5
Answers
The average of numbers is equal to sum of values to number of values.
Determine the average value of observations.
[tex]\begin{gathered} a=\frac{-\frac{2}{5}+\frac{7}{10}+\frac{1}{2}-\frac{1}{5}}{4} \\ =\frac{\frac{-4+7+5-2}{10}}{4} \\ =\frac{\frac{6}{10}}{4} \\ =\frac{3}{20} \end{gathered}[/tex]So average value of the numbers is 3/20.
Find the measure of Zx in the triangle.
21°
The measure of Zx is
(Simplify your answer. Type an integer or a decimal.)
...
Answers
The third angle of the triangle is 87°.
The Pythagorean Theorem is used for finding the length of the hypotenuse of a right triangle.
Pythagoras was a Greek mathematician who discovered that on a triangle abc, with side c being the hypotenuse of a right triangle (the opposite side to the right angle), that: a² + b² = c².Formula for the Base of an Isosceles Triangle
If you know the side length and height of an isosceles triangle, you can find the base of the triangle using this formula: b = 2√a² - h²Equate the sum of all the angle which is equal to 180°.
Sum of triangle = 180°
∠A + ∠B + ∠C =180°
21° + 72° + x = 180°
93° + x = 180°
x = 180° - 93°
x = 87°
Hence, the third angle of the triangle is 87°.
To know more about triangle check the below link:
https://brainly.com/question/64787
#SPJ1
What is the probability of a person who plays equation IQ being in grade 6? Enter the answer as a percentage, round to the nearest tenth place.
Answers
ANSWER
28.3%
EXPLANATION
The total number of people that play Equation IQ is 300 - we can know this by adding either the more right column or the lowest row of the table.
From those people, 85 are in grade 6. The probability of a person that plays Equation IQ being in grade 6 is:
[tex]P(\text{grade 6})=\frac{\#\text{ people in grade 6}}{\#\text{ total number of players}}=\frac{85}{300}\approx0.2833\ldots[/tex]To write it as a percentage we just have to multiply it by 100:
[tex]0.283\times100=28.3\text{ \%}[/tex]a proton is a positively charged particle found in the nuclei of atoms a proton has a diameter of 1.5 x 10^-15 meters How is this written in standard form. A) 0.000000000000015 meters B) 0.0000000000000015 meters C) 0.00000000000000015 meters D)0.000000000000000015 meter
Answers
Trapezoid A'B'C'D was formed after a translation and reflection.YA61AB41D2The amount of unitstrapezoid ABCD wastranslated is the nextnumber of yourcombinationReturn-621D4Α'В"to the-6Dungeon
Answers
The trapezoid on the left side of the y-axis, is first of all moved 6 units down (negative 6 units on the y axis).
Next its moved 6 units to the right (positive 6 units on the x-axis).
Then it rotates 180 degrees clockwise, and the transformation from trapezoid ABCD to A'B'C'D' is complete.
Tim bought a new car for 25,000 one year later the value of the car decrease to 20,000 what is the percentage of the decrease of the car
Answers
Answer:
The percentage decrease in the value of the car is;
[tex]20\text{\%}[/tex]Explanation:
Given that the initial price of the car is;
[tex]25,000[/tex]And after one year the price decreased to;
[tex]20,000[/tex]The percentage change in the price will be;
[tex]\begin{gathered} \text{ \%P }=\frac{25000-20000}{25000}\times100\text{\%} \\ \text{ \%P }=\frac{5000}{25000}\times100\text{\%} \\ \text{ \%P }=0.2\times100\text{\%} \\ \text{ \%P }=20\text{\%} \end{gathered}[/tex]Therefore, the percentage decrease in the value of the car is;
[tex]20\text{\%}[/tex]How many radians are equal to 180 degrees 2piPi 1 2
Answers
Given: An angle of 180 degrees.
Required: To find the measure of the given angle in radians.
Explanation: The degree and radians measure of an angle is related by the following relation
[tex][/tex]Given parallelogram ROCK and m R =159, find m 20.
Answers
Answer:
m∠C = 159
Explanation:
In parallelograms, opposite angles have the measure. Since angle C is opposite to angle R, we can write the following expression:
m∠C = m∠R
m∠R is equal to 159, so m∠C is equal to:
m∠C = 159
So, the answer is m∠C = 159
someone help me
please and thank you
Answers
Answer: Answer C
Step-by-step explanation:
Because it is a reflection of the Y-axis, the X-coordinates would remain the same but the Y-coordinates would change.
The triangle ABC shown on the coordinate plane below,is dilated from the origin by scale factor= 1/2. what is the location of triangle A'B'C'?
Answers
Explanation:
With a dialation about the origin of a scale factor of 1/2 every point of the dialated figure is now one half of the points from the original figure:
[tex](x,y)\rightarrow(\frac{1}{2}x,\frac{1}{2}y)[/tex]We have this points:
• A: (3, 4)
,• B: (-7, 2)
,• C: (2, 2)
The new coordinates of these points will be:
Answer:
• A': (1.5, 2)
,• B': (-3.5, 1)
,• C': (1, 1)
Brady wants to purchase a skateboard that costs $245. So far, he has saved $98 and plans to savean additional $25 per week.Part A:If w represents the number of weeks, write the inequality that represents how many weeks it willtake Brady to save at least $245.
Answers
number of weeks: w
cost of the skateboard: 245
Amount saved: 98
Additional per week: 25
98+25w ≥ 245
Since he have to save at least 245, the expression must be equal or greater to 245
2 and the probability that event A occurs given 2 In an experiment, the probability that event B occurs is 3 6 that event B occurs is 7 What is the probability that events A and B both occur? Simplify any fractions.
Answers
In order to find the probability that events A and B both occurs, we can use the following formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]So we have that:
[tex]\begin{gathered} \frac{6}{7}=\frac{P(A\cap B)}{\frac{2}{3}} \\ 7\cdot P(A\cap B)=6\cdot\frac{2}{3} \\ 7\cdot P(A\cap B)=4 \\ P(A\cap B)=\frac{4}{7} \end{gathered}[/tex]Ahmed takes out a loan charging 6.7% simple interest for 10 years.
At the end of 10 years Ahmed pays back $1278 in just interest. Round your answer
to the nearest penny. The original amount of the loan (principal) was
A/
Round your answer to the nearest penny..
Answers
Answer:
$1907.46
Step-by-step explanation:
You want the principal amount of a 10-year loan that earns $1278 in simple interest at the annual rate of 6.7%.
Simple InterestThe interest is given by the formula ...
I = Prt
Solving for P gives ...
P = I/(rt)
P = $1278/(0.067·10) ≈ $1907.46
The amount of the loan was $1907.46.
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write in slope intercept form and identity the slope and y intercept. a. x/3 + y/2 = 1b. 4x -3y + 2 =0c. x - y = 5(x - y)
Answers
Consider that the slope-intercept form of the straight line with slope (m) and y-intercept (c) is given by,
[tex]y=mx+c[/tex]a.
Modify the given equation as,
[tex]\begin{gathered} \frac{x}{3}+\frac{y}{2}=1 \\ \frac{y}{2}=-\frac{x}{3}+1 \\ y=-\frac{2}{3}x+2 \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=-\frac{2}{3}x+2[/tex]b.
Modify the given equation as,
[tex]\begin{gathered} 4x-3y+2=0 \\ 3y=4x+2 \\ y=\frac{4}{3}x+\frac{2}{3} \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=\frac{4}{3}x+\frac{2}{3}[/tex]c.
Modify the given equation as,
[tex]\begin{gathered} x-y=5(x-y) \\ x-y=5x-5y \\ 5y-y=5x-x \\ 4y=4x \\ y=x \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=x[/tex]A right rectangular prism's edge lengths are 10.5 inches, 5 inches, and 2 inches. How many unit cubes with edge lengths of 0.5 inch can fit inside the prism?A)105 unit cubesB)210 unit cubes460 unit cubesD)840 unit cubes5)
Answers
Given
A right rectangular prism's edge lengths are 10.5 inches, 5 inches, and 2 inches.
To find how many unit cubes of edge length 0.5 inches can fit inside the prism.
Explanation:
It is given that, the volume of the rectangular prism is,
[tex]\begin{gathered} Volume=l\times b\times h \\ =10.5\times5\times2 \\ =105in^3 \end{gathered}[/tex]Since the edge length of 0.5inch.
Then,
[tex]\begin{gathered} Volume\text{ of rectangular prism}=n\times Volume\text{ of a cube} \\ 105=n\times(0.5)^3 \\ n=\frac{105}{0.125} \\ n=840 \end{gathered}[/tex]Hence, the number of cubes is 840 unit cubes.
Debra has ridden 6 miles of a bike course. The course is 15miles long. What percentage of the course has Debra ridden so far
Answers
From the question
Miles covered for bike course = 6 miles
Total miles of course = 15 miles
In percentage, this becomes
Let z = percentage of miles covered
Hence
[tex]z=\frac{\text{miles covered}}{Total\text{ miles}}\times100\text{\%}[/tex]Substitute in the values to get
[tex]z=\frac{6}{15}\times100\text{\%}[/tex]Simplify:
[tex]\begin{gathered} z=\frac{2}{5}\times100\text{\%} \\ z=2\times20\text{\%} \\ z=40\text{\%} \end{gathered}[/tex]Therefore, the percentage of the course Debra has ridden so far is 40%
solve[tex]3 - \frac{x}{2} \geqslant 15[/tex]the equation
Answers
GIVEN:
We are given the following inequality;
[tex]3-\frac{x}{2}\ge15[/tex]Required;
To solve the inequality for x.
Step-by-step solution;
We begin by collecting like terms. Subtract 3 from both sides;
[tex]\begin{gathered} 3-3-\frac{x}{2}\ge15-3 \\ \\ -\frac{x}{2}\ge12 \end{gathered}[/tex]Now we cross multiply;
[tex]-x\ge24[/tex]We now multiply both sides of the inequality by -1.
Note that when an inequality is multiplied or divided by a negative value, then the inequality sign flips over.
Therefore;
[tex]\begin{gathered} -x\ge24 \\ \\ -x(-1)\ge24(-1) \\ \\ x\leq-24 \end{gathered}[/tex]ANSWER:
[tex]x\leq-24[/tex]8. The square of a number decreased by 3 times the number is 28. Find allpossible values for the number.
Answers
We need to find a number x
We know its square (x²) decreased by 3 times it (3x) is 28. Then
x² - 3x = 28
x² - 3x - 28 = 0 [Simplifying the equation]
Since - 7 + 4 = - 3 and (-7) (4) = - 28, we factor the polynomial:
(x - 7)(x + 4) = 0 [Factoring the polynomial]
When a multiplication, like (x - 7)(x + 4), equals cero?
it equals cero if and only if
(x - 7) = 0 or (x + 4) = 0
Then, simplifying both equations
x = 7 or x = - 4
Answer: x = 7 or x = - 4