Consider the following two cash flow series of payments: Series A is a geometric series increasing at a rate of 9.5% per year. The initial cash payment at the end of year 1 is $1,000. The payments occur annually for 5 years. Series B is a uniform series with payments of value X occurring annually at the end of years 1 through 5. You must make the payments in either Series A or Series B.
a. Determine the value of X for which these two series are equivalent if your TVOM is i = 9%. $
b. If your TVOM is 8%, would you be indifferent between these two series of payments? Enter the PW for each series to support this choice.
c. If your TVOM is 5%, would you be indifferent between these two series of payments? Enter the PW for each series to support this choice.
Answers
Answer:
Step-by-step explanation:
From the given information;
The present value of series A:\(=\Big[1000 \times \dfrac{(1.095)^0}{(1.09)^1}\Big]+\Big[1000 \times \dfrac{(1.095)^1}{(1.09)^2}\Big]+...+\Big[1000 \times \dfrac{(1.095)^4}{(1.09)^5}\Big]\)
\(= 1000 \Big [ \dfrac{1}{1.09}+ \dfrac{1.095}{1.1881}+ \dfrac{1.199}{1.295}+\dfrac{1.313}{1.912}+\dfrac{1.438}{1.539}\Big]\)
\(= 1000 \Big[ 0.917 + 0.922 + 0.926 + 0.930 + 0.934\Big]\)
\(= 1000 \times 4.629\)
\(= \$4629\)
Thus, the present value of series A is = $4629
Present value of series A = Present value of series B
\(The \ value \ of\ X = \dfrac{Present \ value \ of \ series \ B }{\Big [\dfrac{1-(1+r)^{-n}}{r} \Big ]}\)
\(The \ value \ of\ X = \dfrac{4629 }{\Big [\dfrac{1-(1+0.09)^{-5}}{0.09} \Big ]}\)
\(The \ value \ of\ X =\dfrac{4629 \times 0.09}{1-0.6499}\)
\(The \ value \ of\ X =\dfrac{416.61}{0.3501}\)
\(The \ value \ of\ X =1189.97\)
Thus, the value of X = $1189.97
2.
The present value of series A:
\(=1000 \times \Big[\dfrac{(1.095)^0}{(1.08)^1}+ \dfrac{(1.095)^1}{(1.08)^2}+...+\dfrac{(1.095)^4}{(1.08)^5}\Big]\)
\(=1000 \Big [ \dfrac{1}{1.08}+ \dfrac{1.095}{1.1664}+\dfrac{1.199}{1.2597}+\dfrac{1.313}{1.3605}+\dfrac{1.438}{1.4693}\Big ]\)
\(= 1000\Big [ 0.9259 + 0.9839+0.952 + 0.965+0.979\Big ]\)
\(= 1000 \times 4.76059\)
\(\simeq \$4761\)
Thus, the present value of series A is = $4761
Present value of series B =\(Value \ of \ X \times \Big [ \dfrac{1 - (1+r)^{-n} }{r}\Big ]\)
\(= 1189.97 \times \Big [ \dfrac{1 - (1+0.08)^{-5} }{0.08}\Big ]\)
\(= \dfrac{1189.97}{0.08} \times \Big ( 1 -0.6806\Big )\)
\(= 14874.625 \times 0.3194\)
\(= \$4750\)
Thus, the present value of series B = $4750
3.
The present value of series A:
\(=1000 \times \Big[\dfrac{(1.095)^0}{(1.05)^1}+ \dfrac{(1.095)^1}{(1.05)^2}+...+\dfrac{(1.095)^4}{(1.05)^5}\Big]\)
\(=1000 \Big [ \dfrac{1}{1.05}+ \dfrac{1.095}{1.1025}+\dfrac{1.199}{1.1576}+\dfrac{1.313}{1.2155}+\dfrac{1.438}{1.276}\Big ]\)
\(= 1000\Big [ 0.9524 + 0.9932+1.0357 + 1.08+1.127\Big ]\)
\(= 1000 \times 5.1883\)
\(\simeq \$5,188\)
Thus, the present value of series A = $5188
Present value of series B: =\(Value \ of \ X \times \Big [ \dfrac{1 - (1+r)^{-n} }{r}\Big ]\)
\(= 1189.97 \times \Big [ \dfrac{1 - (1+0.05)^{-5} }{0.05}\Big ]\)
\(= \dfrac{1189.97}{0.05} \times( 0.2165)\)
\(= \$5152.57\)
Thus, the present value of series B = $5153
Related Questions
HELP ME please. i dont understand this.
Answers
Answer:
Step-by-step explanation:
Perimeter add all the sides.
so let's walk around and combine like terms:
starting on the bottom moving to the left.
3x^2 + x^2= 4x^2 (there are no other squared terms)
back to the bottom moving left again:
-11x-3x+3x+x = -10x (-3x + 3x =0)
so -11x + x = -10x
now add all of the constants
-1 + 2 = 1
so your answer is
4x^2 -10x + 1
What is the solution to (x – 3)^3(x+ 1)(x - 2)<0?
Answers
Answer:
i have no answer
Step-by-step explanation:
(((x-3²)•3)•(x+1))•(x-2)<0
(3•(x-9)•(x+1))•(x-2)<0
3•(x-9)•(x+1)•(x-2)<0
3•(x-9)•(x+1)•(x-2)<0
Answer:
B
Step-by-step explanation:
Got it on edge
Use the Distributive Property to rewrite each algebraic expression.
15(2 + r)
Answers
Using the distributive property, the algebraic expression 15(2 + r) can be rewritten as: 30 + 15r.
How to Use the Distributive Property to Rewrite an Algebraic Expression?To use the distributive property to rewrite an algebraic expression, you need to multiply the value outside the parentheses by each value inside the parentheses.
For example, if you have the expression "a(b + c)", you would use the distributive property to rewrite it as "ab + ac".
15(2 + r) (given)
15 * 2 + 15 * r
30 + 15r
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42. Estimate: 48293 - 39
Answers
Answer:
48293-39≈48290-40
=48250
I need this answer pls
Answers
Which expressions are completely factored?
Select each correct answer.
Responses
16a5−20a3=4a3(4a2−5)
16 a begin power 5 end power minus 20 a cubed equals 4 a cubed left parenthesis 4 a squared minus 5 right parenthesis
12a3+8a=4(3a3+2a)
12 a cubed plus 8 a equals 4 left parenthesis 3 a cubed plus 2 a right parenthesis
30a6−24a2=3a2(10a4−8)
30 a begin power 6 end power minus 24 a squared equals 3 a squared left parenthesis 10 a begin power 4 end power minus 8 right parenthesis
24a4+18=6(4a4+3)
24 a begin power 4 end power plus 18 equals 6 left parenthesis 4 a begin power 4 end power plus 3 right parenthesis
Answers
The expressions that are completely factored are:
16a5−20a3=4a3(4a2−5) is correct.12a3+8a=4(3a3+2a) is correct.24a4+18=6(4a4+3) is correct.Why are they considered to be correct?The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.
For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.
Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).
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Answer:
16a^5−20a^3=4a^3(4a^2−5)
and
24a^4+18=6(4a^4+3)
Step-by-step explanation:
What is 87.9 to the square root of 6
Answers
Answer:
57780.4353288
Step-by-step explanation:
The square root to the square root of 6 is 57780.4353288
Hope it helped! :)
May i have brainliest!
how do you know if an number composite or not
Answers
Answer:
A prime number has only two factors: 1 and itself. A composite number has more than two factors
Step-by-step explanation:
Can i have a thanks?
GEOMETRY 100 POINTS
Find the length of BC
Answers
Answer:
x = 16
Step-by-step explanation:
Opposite sides are equal in a parallelogram
AD = BC
5x - 12 = 3x + 20
5x - 3x = 20 + 12
2x = 32
x = 32/2
x = 16
PLEASE HELP ASAP WILL MARK BRAINLIEST !
Write the number in scientific notation.
83,497.6
x 10
Answers
Answer: 834,976
Step-by-step explanation:
Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 2 million barrels of oil in the well; six years later 1,000,000 barrels remain.
Required:
a. At what rate was the amount of oil in the well decreasing when there were 1,200,000 barrels remaining?
b. When will there be 100,000 barrels remaining?
Answers
Answer:
A. It was decreasing by -138,629.44 barrels
B. 26 years of time
Step-by-step explanation:
Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.
A. At 1200000
Bt = 1200000
-1/6ln2 x 1200000
Solve this using a calculator
= -138,629.4361
So the amount of oil is decreasing by -138,629.44 barrels
On a coordinate plane, how are the locations of the points (-4 , 8) and (-4 , -8) related?
A.
reflection across the y-axis
B.
reflection across the x-axis
C.
reflection across both axes
D.
locations unrelated
Answers
Answer:
A. reflection across the y-axiss
Step-by-step explanation:
Given:
The locations of the two points are (-4 , 8) and (-4 , -8).
To find:
The relation between two points.
From the given points (-4, 8) and (-4 , -8), it is clear that the y-coordinates are same but the sign of x-coordinates are opposite.
If a figure is reflected across the y-axis, then we change the sign of x-coordinate and the y-coordinates remain same, i.e.,
\((x,y)\)→\((-x,y)\)
For (-4,8)
\((-4,8)\)→ \((-4,-8)\)
So, it is reflection across the y-axis.
Therefore, the correct option is A.
Simon spends £28 over 7 days. Each day, he spends 50p more than the previous day.
How much did Simon spend on day 1?
Answers
The amount of money Simon spent on day 1 of the 7 days is that;
He spent £25 on the first day.
We are told he had spent £28 over 7 days.Each day, he spends 50 pence more than the previous day. This means that;
From conversion,1 pound = 100 pence
Thus, 50 pence = (50 × 1)/100 = £0.5
If the money he spent on the first day is £x.On second day, he would have spent a total of; £(x + 0.5)On third day; x + 0.5 + 0.5= x + 1On fourth day; x + 1 + 0.5 = x + 1.5On fifth day; x + 1.5 + 0.5 = x + 2On sixth day; x + 2 + 0.5 = x + 2.5On seventh day; x + 2.5 + 0.5 = x + 3Thus; x + 3 = 28x = 28 - 3
x = £25
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What is the equation of this line in Slope intercept Form?
Answers
Answer:
y = x - 5
Step-by-step explanation:
Hell please please please
Answers
Then find the volume of the cylinder which is 549.78 in
Then add them together - 32.725 + 549.78 = 582.505
Finally round it to the nearest whole number which is 583
The final answer should be 583
Graph the equation. Identify the intercepts.
1.) y + 2 = -4(x - 2)
x-int:
y-int:
Answers
For the following equation, the x-intercept is (3/2, 0) and the y-intercept is (0, 6).
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Here,
y+2=-4(x-2)
for x-intercept=(x,0)
2=-4(x-2)
2=-4x+8
4x=6
x=6/4=3/2
for y-intercept=(0,y)
y+2=-4(*-2)
y=6
The x-intercept is (3/2,0) and y-intercept is (0,6) for given equation.
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the rectangle below has an area of x^2 8x 15x 2 8x 15x, squared, plus, 8, x, plus, 15 square meters and a width of x 3x 3x, plus, 3 meters. what expression represents the length of the rectangle? a rectangle with a width of x plus three and an unknown length. the area of the rectangle is x squared plus eight x plus fifteen.
Answers
The expression that represents the length of the rectangle is x + 5
What is meant by Area of a rectangle?Dimensions of a rectangle. A = l × b. Once a rectangle's length and breadth are known, its area may be computed. The rectangle's area can be measured in square units by multiplying the length and width. The region that a rectangle occupies in a two-dimensional space is known as a rectangle's area. Another way to describe a rectangle's area is the quantity of square units needed to fill it entirely. The whole distance around the outside of a rectangle is referred to as the rectangle's perimeter.The area of a rectangle is described as follows:
area = lw
where
l = length
w = width
Therefore,
area = x² + 8x + 15
w = x + 3
Therefore,
x² + 8x + 15 = (x + 3)l
divide both sides by x + 3
l = x² + 8x + 15 / x + 3
l = (x+3)(x+5) / (x + 3)
Finally,
length = x + 5
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You tell a number of friends about an interesting video you saw online. Each of those
friends tell the same number of friends about it. This pattern continues, and there are
no repeats in the people told. The numbers of people who hear about this video
through you form a geometric sequence. There are 243 people in the fifth round and
2187 people in the seventh round.
Answers
Answer:
okay ummm NBA youngboy Kacey talk
Step-by-step explanation:
School starts at 2:50 pm. The school day is 6 hours and five minutes when does school start
Answers
Answer:
845 am
Step-by-step explanation:
Answer:
8:45 Am
Step-by-step explanation:
How many pounds are in 1
1⁄2 pounds and 8 ounces?
There are
pounds in 1 pounds and 8 ounces.
The solution is
n ID:
Answers
The number of pounds in \(1\frac{1}{2}\) pounds and and 8 ounces is 2 pounds.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 1 pound = 16 ounces.
As there are \(1\frac{1}{2}\) pounds=1.5×16= 24 ounces.
The total number of ounces in \(1\frac{1}{2}\) pounds and 8 ounces is
24+8
32 ounces.
Now let us convert Ounces to pounds.
we divide the number of ounces by 16.
Therefore, 32 ounces is equal to 32/16 = 2 pounds.
Hence, 2 pounds will be there in \(1\frac{1}{2}\) pounds and 8 ounces
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What is the value of n?
Enter your answer in the box.
n = __ cm
Answers
The value of the missing segment n using the product of intersecting chord theorem is 14cm
Using the product of intersecting chord principleThe product of the segments of two intersecting chords are equal.
The segments of the chords ;
Chord 1 = 4 and n
Chord 2 = 7 and 8
The principle can be related Mathematically thus ;
4 × n = 7 × 8
4n = 56
Divide both sides by 4
4n/4 = 56/4
n = 14
Therefore, the value of n in the question is 14cm
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Fill in the table using this function rule.
y=-3x-3
X
-2
-1
0
1
y
0
0
0
X
Ś
Answers
Answer:
X | y
---------------
-2 | 3
-1 | 0
0 | -3
1 | -6
Is a triangle with sides of 5 meters, 12 meters, and 13 meters a right triangle? Explain/Show your work.
Answers
Answer:
Step-by-step explanation:
given g(x)=5x+3, find g(4)
Answers
Answer:
g(4) = 23
Step-by-step explanation:
g(x)=5x+3, find g(4)
g(4) = 5(4) + 3
g(4) = 20 + 3
g(4) = 23
Hope that helps!
Answer:
\( \boxed{g(4) \: is \: 23}\)
Step-by-step explanation:
given :
g(x) = 5x + 3
find g(4)
Answer :
substitute 4 into the equation of function
\( g(x) = 5x + 3\)
\(g(4) = 5(4) + 3\)
\(g(4) = 20 + 3\)
\(g(4) = 23\)
Find the x-intercepts and y-intercept of the following function.
f(x) = (x+9) (x +9) (x-8)
Answers
Answer:
To find the x-intercepts, we set y = 0 and solve for x:
f(x) = (x+9) (x+9) (x-8) = 0
The solutions are x = -9 (double root) and x = 8.
To find the y-intercept, we set x = 0:
f(0) = (0+9) (0+9) (0-8) = -583.
Therefore, the y-intercept is (0, -583).
drag tiles to the boxes to form correct pairs. match the cube roots and square roots with their values.
Answers
the cubed root of 729 is 9
the square root of 100 is 10
the cubed root of 216 is 6
the square root of 64 is 8
and the cubed root of 343 is 7
This should be right
____________ is a test of a single population and is to determine if there is an association between two characteristics of that population. A) The chi-square test for independence B) Pearson product moment test C) The chi-square test for homogeneity D) Goodness-of-fit test E) Welch’s t test
Answers
The option a "The chi-square test for independence" is correct.
In the given question we have to find, a test of a single population and is to determine if there is an association between two characteristics of that population.
The given options are
A) The chi-square test for independence
B) Pearson product moment test
C) The chi-square test for homogeneity
D) Goodness-of-fit test
E) Welch’s t test
As we know that;
When a categorical variable has more than two levels, a chi-square test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.
So, the chi-square test for independence is correct answer.
Option (B) and (E) are two-sample tests.
(C) involves two attributes.
(D) Doesn't check association.
Hence all these are incorrect.
So the option a "The chi-square test for independence" is correct.
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What is the surface area of the sphere shown below with a radius of 7?
1
7
A. 49, sq. units
B. 65 sq. units
C. 196 sq. units
D. 457 sq. units
SUBMIT
Answers
Answer:
c
Step-by-step explanation:
the surface area for spheres is
4 × π × r²
4 × π × (7²) = 196 π
(6.2 x 10²) x (3.5 x 10³)
Answers
Answer:
\(21.7 x 10^5\)
Step-by-step explanation:
(6.2 x 10²) x (3.5 x 10³)
First, multiply the coefficients: 6.2 x 3.5 = 21.7.
Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.
Therefore, the result is 21.7 x 10^5.
Answer:
3286000
Step-by-step explanation:
PLS HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the solution to the equation given the replacement set?
25 - 3r = 10; {3, 4, 5, 6,}
Responses
3
4
5
6
Answers
Answer:
r = 5
Step-by-step explanation:
25 - 3r = 10 ( subtract 25 from both sides )
- 3r = - 15 ( divide both sides by - 3 )
r = 5
the solution from the replacement set is 5