Mathematics College

5.
Find the present value of the annuity.

Amount Per Payment: $6,225

Payment at End of Each: Quarter

Number of Years: 6

Interest Rate: 8%

Compounded: Quarterly

Answers

Answer 1
To solve this we are going to use the present value of annuity formula: [tex]PV=P[ \frac{1-(1+ \frac{r}{n})^{(-kt)} }{ \frac{r}{n} }] [/tex]
where
[tex]PV[/tex] is the present value 
[tex]P[/tex] is the periodic payment
[tex]r[/tex] is the interest rate in decimal form 
[tex]n[/tex] is the number of times the interest is compounded per year 
[tex]k[/tex] is the number of payments per year 
[tex]t[/tex] is the number of years

We know for our problem that [tex]P=6225[/tex] and [tex]t=6[/tex]. To convert the interest rate to decimal form, we are going to divide it by 100%:
[tex]r= \frac{8}{100} [/tex]
[tex]r=0.08[/tex]
Since the interest is compounded quarterly, it is compounded 4 times per year, so [tex]n=4[/tex]. Similarly, since the payment is made at the end of each quarter, it is made 4 times per year; therefore, [tex]k=4[/tex]. 
Lets replace the values in our formula:
[tex]PV=P[ \frac{1-(1+ \frac{r}{n})^{(-kt)} }{ \frac{r}{n} }] [/tex]
[tex]PV=6225[ \frac{1-(1+ \frac{0.08}{4})^{(-(4)(6)} }{ \frac{0.08}{4} }] [/tex]
[tex]PV=117739.19[/tex]

We can conclude that the present value of the annuity is $117,739.19


Related Questions

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 108x + 6, [−3, 4]

Answers

It is convenient to use a graphing calculator for this. The graph shows the maximum and minimum are not at the ends of the interval, so could be found by differentiating the function and setting that derivative to zero. The function would then need to be evaluated for those solutions {-2, 3}.

The absolute minimum on the interval is -237 at x=3.
The absolute maximum on the interval is 138 at x=-2.

Answer:

The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.

Step-by-step explanation:

To find the absolute extrema values of [tex]f(x) = 6x^3 - 9x^2 - 108x + 6[/tex]  on the closed interval [−3, 4] you must:

1. Locate all critical values. We need to find the derivative of the function and set it equal to zero.

[tex]\frac{d}{dx}f(x)= \frac{d}{dx}\left(6x^3-9x^2-108x+6\right)=\\\\f'(x)=\frac{d}{dx}\left(6x^3\right)-\frac{d}{dx}\left(9x^2\right)-\frac{d}{dx}\left(108x\right)+\frac{d}{dx}\left(6\right)\\\\f'(x)=18x^2-18x-108[/tex]

[tex]18x^2-18x-108=0\\18\left(x^2-x-6\right)=0\\18\left(x+2\right)\left(x-3\right)=0\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=-2,\:x=3[/tex]

2. Evaluate f(x) at all the critical values and also at the two values -3 and 4

[tex]\left\begin{array}{cc}x&f(x)\\-3&87\\-2&138\\3&-237\\4&-186\end{array}\right[/tex]

3. The absolute maximum of f(x) on [-3, 4] will be the largest number found in Step 2, while the absolute minimum of f(x) on [-3, 4] will be the smallest number found in Step 2.

Therefore,

The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.

Heong cut a slice of birthday cake. The slice formed the angle shown. What is the measure of the angle shown?

Answers

Do you have a picture?

Hey can you please help me posted picture of question

Answers

you have 2 outcomes per flip ( heads or tails)

you are flipping the coin 3 times

 so there is 2^3 outcomes = 8 leaves required
two outcomes per coin, 2/coin

3 coins

so 2^3 = 8; 

the answer is A. 8 leaves

Problem:
The standard form of a circle is (x-h)2+(y-k)2=r2 and for the parabola, y-k=a(x-h)2. The (h,k) pair will be the center of the circle and the vertex of the parabola. The radius of the circle is ‘r’ and the focal length of the parabola is f=1/(4a). For the following General Conic Equation: x2+y2-4x-6y-12=0 complete the following problems showing all your work:

A-Complete the square showing all your work to convert to Standard Form:

B-If this is a circle, state the coordinates of the center and give the radius. If this is a parabola, state the coordinates of the vertex and give the focal length. Show all your work.

C -Sketch the Conic. Label the values you found in part B. Be sure to draw or show the radius or focal length.

Answers

we have that
x²+y²-4x-6y-12=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x²-4x)+(y²-6y)=12

Complete the square twice. Remember to balance the equation by adding the same constants to each side

(x²-4x+4)+(y²-6y+9)=12+4+9

Rewrite as perfect squares

(x-2)²+(y-3)²=25

the answer part A) is 

(x-2)²+(y-3)²=5²-----> this is the standard form of the equation of a circle

Part B) (x-2)²+(y-3)²=5²

the center is the point (2,3) and the radius is r=5 units


Part C) 

using a graph tool

see the attached figure

Hey can you please help me posted picture of question

Answers

A compound event is defined as an event which has more than 1 possible outcomes.

In given case, Karen has to find the probability of a number greater than 4 which can appear when a die is rolled. The possible outcomes in this case are 2 i.e. 5 and 6

Since, the number of possible outcomes is more than 1, the event is a compound event.

So answer is true

It took Alex 2.5 hours to cover a certain route walking at a rate of 3.6 km/h. How long would it take Alex to cover the same route if he walked at a rate of 4.5 km/h

Answers

It will take Alex 2 hours strolling a similar course at 4.5 km/h in light of the fact that 3.6km/h times 2.5 hours was 9km, so 9km separated by 4.5km/h is 2 hours.

Answer:

2 hours

Step-by-step explanation:

Identify the figure shown and find its surface area. Explain how you found your answer.

Answers

This is a triangle prism, the base is a square and the four sides are equal triangles.

To find the surface area you need to first find the areas of the triangles, then the square, in the end you have to add them together.

Since we know the area of a triangle is 1/2bh we know that one if the triangle in the figure is
9*16/2=72(in^2)
there are four of these so we multiply it by 4
4*72=288(in^2 aka squared inches)

Then we need to find the area of the square. side * side=9*9=81 (in^2)

Add them together we get the surface area.
288+81=369 (in^2)

hey can you please help me posted picture of question

Answers

Answer:
The solutions are: 
[tex] \frac{3 + i}{2} [/tex] and [tex] \frac{3 - i}{2} [/tex]

Explanation:
The general form of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
2x² - 6x + 5 = 0

By comparison:
a = 2
b = -6
c = 5

Now, to get the solutions of the equation, we will have to use the quadratic formula shown in the attached image.

By substituting in the formula, we would find that:
either x = [tex] \frac{6 + \sqrt{(-6)^2 - 4(2)(5)} }{2(2)} = \frac{3 + i}{2} [/tex]

or x = [tex] \frac{6 - \sqrt{(-6)^2 - 4(2)(5)} }{2(2)} = \frac{3 - i}{2} [/tex]

Hope this helps :)

A homeowner plants two flowerbeds around his garage. What is the total area he will have planted. Round to nearest tenth.

Answers

We need data to answer

Vernon has obtained a $105,000, 5/1 30-year ARM at 5%. During the first 3 years, he has an option of paying interest only. If he accepts this offer, what would be his initial payment?

Answers

The answer is $437.50. (APEX)

Answer: 437.50

Step-by-step explanation:

What is the vertex of the quadratic y=-2x^2-4x-5

Answers

y=-2x²-4x-5

We will need to complete square to write the equation in the vertex form.

y=-2(x²+2x)-5
y=-2(x²+2x+1)-5+2
y=-2(x+1)² - 3
Vertex (-1,-3)

Answer:

(-1,-3)

Step-by-step explanation:

I just took the test, and I got 100%!!!

the scatter plot shows the number of students per class al monida middle school and the number of magazine subscription each class sold for a fund raiser.About how many subscription did the class of 30 students sell

Answers

For this case, the first thing to do is to observe the value that the function takes on the axis y, when on the x axis we have 30 students.
 We have then:
 For x = 30:
 The value of y is given by:
 y = 175 (approximately)
 Answer:
 y = 175 subscriptions
From the question,
About how many subscription did the class of 30 students sell,
We need to consider the Given which is x = 30:
So The value of y is given by:
y = 175 (approximately)

So the answer would be the third option.

Help with the graph and answer below

Answers

The number of real zeros are equal to the x-intercepts of the graph. x-intercepts are the points where the graph crosses the x-axis.

From the graph we can see that the function does not cross the x-axis at any point. Hence it has no x-intercept and thus no real zero. Both the zeros will be complex. 

So, the correct answer is option B.
Function has exactly 2 complex solutions. 
The graph shows a parabola. A parabola's equation is f(x) = 4a*x^2 + b

This means that 1 value of y  is equal to two values of x

so the answer is D. Function f has two real solutions

The ratio of sugar to flour is 2:3. If there are 6 cups of sugar, how many cups of flour are there

Answers

The answer would be 9 cups of flour
(5/1)=(2/x)
cross multiply
5x=2x1
simplify
5x=2
divide each side by 5 to find x
x=2/5
2/5 or 0.4 cups of flour are needed
answer= 2/5

Which of the following holds about 800 milliliters o f water?

Answers

probably the dog bowl. 800ml is about 3.4 US cups

The function F(x) = log0.5 x is increasing. The answer is B. False. Just finished taking the quiz I had guessed.
A. True
B. False

Answers

False on Apex, I need 20 characters to finish the answer. 


Answer:

The statement is false

B is correct

Step-by-step explanation:

Given: [tex]f(x)=\log_{0.5}x[/tex]

Increasing function.

Log function:

[tex]y=\log_ax[/tex]

If 0<a<1 then y is decreasing function.

If a>1 then y is increasing function.

Now, we compare the given function

[tex]\log_ax\rightarrow \log_{0.5}x[/tex]

a=0.5

0.5<1

If 0<a<1 then y is decreasing function.

Therefore, f(x) is decreasing. But we are given f(x) is increasing.

Hence, The statement is false

how do the graphs of f(x)=x^3 and g(x)=(1/3x)^3 relate?

Answers

Both graphs have the same exponential degree of 3. The only difference between the two is that g(x) is expanded to a scale factor of 3, due to the coefficient being 1/3. 
Graph of g(x) is the transformation of the graph of f(x) The graph of f(x) is: while of g(x) is graphed We can see the g(x) is f(x) after a reflection on the y-axis and a horizontal compression by a factor of 1/3

There are 2,000 eligible voters in a precinct. 548 of the voters are randomly selected and asked whether they planned to vote for the democratic incumbent or the republican challenger. of the 548 surveyed, 474 said they would vote for the democratic incumbent. using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the democratic incumbent?

Answers

Sample size, n = 548
Point estimate, p = 474/548 = 0.865 or 86.5%
Z at 0.99 confidence coefficient = 2.58

Confidence limits = p +/- Z*Sqrt [p(1-p)/n] = 0.865 +/- 2.58 Sqrt [0.865(1-0865)/548] = 0.865 +/- 0.0378 = (0.8272,0.9028) or (82.72%,90.28)

Which of these shows 8 + 3m rewritten using the commutative property of addition? 8m + 3 8 − 3m 3m − 8 3m + 8

Answers

Ans:- 4th option (3m + 8)

Reason:

★Commutative Property★

The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around.

For addition, the rule is:
"a + b = b + a"

Hope this helps!

Answer:(3m+8)

Step-by-step explanation:

solve the system of equations 5x-2y=88 3x+4y=58 show all work

Answers

The given equations are:

5x - 2y = 88
3x + 4y =  58

Multiplying the 1st equation by 2, we get the new set of equations as:

10x - 4y = 176
3x + 4y = 58

Adding the two equations, we get:

10x - 4y + 3x + 4y = 176 + 58
13x =234
x =  18

Using the value of x in 1st equation, we get:

5(18) - 2y = 88
- 2y = 88 -5(18)
-2y = -2
y = 1

So, the solution of the equation is (18, 1)

[tex]\left\{\begin{array}{ccc}5x-2y=88&1^o\\3x+4y=58&2^o\end{array}\right\\\\1^o\ 5x-2y=88\ \ \ \ |\text{subtract 5x from both sides}\\-2y=-5x+88\ \ \ |\text{divide both sides by (-2)}\\y=2.5x-44\\\\\text{substitute the value of y to the equation}\ 2^o[/tex]

[tex]3x+4\cdot(2.5x-44)=58\\3x+10x-176=58\\13x-176=58\ \ \ |\text{add 176 to both sides}\\13x=234\ \ \ \ |\text{divide both sides by 13}\\x=18\\\\\text{substitute value of x to the equation}\ 1^o\\\\y=2.5\cdot18-44=45-44=1\\\\Answer:\ \boxed{\left\{\begin{array}{ccc}x=18\\y=1\end{array}\right}[/tex]

One endpoint of a line segment is at (4, 2). The line is bisected by placing the midpoint of the line segment at (−2, −1). What are the coordinates of the other endpoint?

A) (−4, −6)
B)(−8, −4)
C)(10, 5)
D)(−8, 4)

Answers

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 4 &,& 2~) % (c,d) &&(~ x &,& y~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+4}{2}~~,~~\cfrac{y+2}{2} \right)=\stackrel{midpoint}{(-2~~,~~-1)}\implies \begin{cases} \cfrac{x+4}{2}=-2\\\\ x+4=-4\\ \boxed{x=-8}\\ ----------\\ \cfrac{y+2}{2}=-1\\\\ y+2=-2\\ \boxed{y=-4} \end{cases}[/tex]
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