treasury securities are issued and backed by the u.s. government and, therefore, are considered to be the lowest-risk securities on the market. as an investor looking for protection against inflation, you are considering the purchase of inflation-adjusted bonds known as u.s. treasury inflation-protected securities (tips). with these securities, the face value (which is paid at maturity) is regularly adjusted to account for inflation; however, the semiannual interest payment (called the bond dividend) remains the same. you purchased a 10-year $10,000 tips bond with dividend of 4% per year payable semiannually (i.e., $200 every 6 months). assume there is no inflation adjustment for the first 5 years, but in years 6 through 10, the bond face value increases by $1150 each year. you use an expected investment return of 14% per year compounded semiannually. note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. what is the net amount of money that you will have received during the 10-year life of the bond without any consideration of dividend reinvestment? the total net amount of money that you would have received is $
Answers
The net amount of money that you will have received during the 10-year life of the bond without any consideration of dividend reinvestment can be calculated by considering the semiannual interest payments and the inflation-adjusted face value of the bond.
The total net amount of money that you would have received is $17,750. The calculations are done as follows:
First, let's calculate the total interest payments over the 10-year period. The bond has a face value of $10,000 and a dividend rate of 4% per year payable semiannually. Since there are two interest payments per year, the semiannual interest payment is $200 ($10,000 * 4% / 2)
Over the first 5 years, there is no inflation adjustment, so the face value remains at $10,000.
Therefore, the total interest payments for these 5 years would be:
5 years * 2 payments per year * $200 per payment = $2,000.
In years 6 through 10, the face value increases by $1,150 each year. So, the face value at the end of year 6 would be $11,150, at the end of year 7 would be $12,300, and so on.
The total interest payments for these 5 years would be:
5 years * 2 payments per year * $200 per payment = $2,000.
Now, let's calculate the total face value at the end of the bond's life. At the end of year 5, the face value is $10,000. From year 6 to year 10, the face value increases by $1,150 each year.
So, the total face value at the end of year 10 would be:
$10,000 + $1,150 + $1,150 + $1,150 + $1,150 + $1,150 = $15,750.
Therefore, the net amount of money that you will have received during the 10-year life of the bond without any consideration of dividend reinvestment is the sum of the interest payments and the face value:
Total interest payments = $2,000
Total face value = $15,750
Net amount = Total interest payments + Total face value
Net amount = $2,000 + $15,750
Net amount = $17,750.
So, the total net amount of money that you would have received is $17,750.
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Related Questions
Opposite angles formed by two intersecting lines are called _______ angles.
Answers
Answer: vertical angles
these angles are also congruent
hope this helps!
Answer:
vertical lines
Step-by-step explanation:
that's answer choice
?
A sprinter travels a distance of 100 m in a time of 9.67 seconds.
What is the sprinter's average speed rounded to 4 sf?
Answers
Answer:
average speed of sprinter will be 10.42m/s
Step-by-step explanation:
distance covered=s=100m
time taken=t=9.67m/s
average speed=10.42m/s
y=x^2-3 graph the function
Answers
vertex (0,-3)
Other points (1,-2) (-1,-2)
Jessica's sister Deborah seems to only need six hours of sleep each night to be well rested. Jessica needs 8 hours most nights, but sometimes she
needs 9 or 10 hours to feel rested enough. How many hours of sleep should Jessica be getting EACH night?
O A. As many as Deborah
O B. No more than eight
O C. No less than 9 or 10
O D. Enough to feel rested
Answers
Answer:
The correct answer is D. Enough to feel rested.
Customers can pick their own cherries at cherry hill. they pay $4 to enter the farm and $3.50 per pound for the cherries they pick. write an equation to model the total cost, y, for x pounds of cherries
Answers
Answer:
The Equation would be $4 + $3.50x = y
Step-by-step explanation:
need the answer please help
Answers
Answer:
the 2nd option
Step-by-step explanation:
given a quadratic in standard form : y = ax² + bx + c (a ≠ 0 )
• if a > 0 then minimum turning point
• if a < 0 then maximum turning point
the graph here has a minimum turning point , so
the function has a positive leading coefficient.
the function is symmetrical about the y- axis , so is of even degree
the function has 1 turning point at (0, 2 )
the graph does not cross the x- axis so has 0 x- intercepts
A frisbee is thrown into the air with an initial velocity of 40 feet per second. The release point is 5 feet above the ground. The function ℎ = −16푡 2 +40푡 + 5 represents the height h in feet of the frisbee after t seconds. (Answer both questions)(PHoto below)
Answers
a) The height of the frisbee each second it is in the air are 5, 29, 45, 53, 53, 45, 29, 5, -27 and -67.
b) The frisbee is in the air for a total of 8 seconds.
To find the height of the frisbee each second it is in the air, we need to substitute different values of t into the equation \(h = -16t^2 + 40t + 5\) and calculate the corresponding height.
a) Let's substitute t = 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 into the equation:
When t = 0: \(h = -16(0)^2 + 40(0) + 5 = 5\)
When t = 1: \(h = -16(1)^2 + 40(1) + 5 = 29\)
When t = 2: \(h = -16(2)^2 + 40(2) + 5 = 45\)
When t = 3: \(h = -16(3)^2 + 40(3) + 5 = 53\)
When t = 4: \(h = -16(4)^2 + 40(4) + 5 = 53\)
When t = 5: h = \(-16(5)^2 + 40(5) + 5 = 45\)
When t = 6: h = \(-16(6)^2 + 40(6) + 5 = 29\)
When t = 7: h = \(-16(7)^2 + 40(7) + 5 = 5\)
When t = 8: h = \(-16(8)^2 + 40(8) + 5 = -27\)
When t = 9: h =\(-16(9)^2 + 40(9) + 5 = -67\)
b) The frisbee is in the air as long as its height is greater than 0. From the calculations above, we can see that the frisbee is in the air from t = 0 to t = 7, inclusive.
Note: The table you provided shows the height of the frisbee at each second it is in the air, but it seems to be cut off. However, based on the calculations above, the height values at each second should be as follows:
0 seconds: 5 feet
1 second: 29 feet
2 seconds: 45 feet
3 seconds: 53 feet
4 seconds: 53 feet
5 seconds: 45 feet
6 seconds: 29 feet
7 seconds: 5 feet
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The graph of the function f(x) = (x + 2)(x − 4) is shown. On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (1, negative 9), and goes through (4, 0). Which describes all of the values for which the graph is negative and increasing? all real values of x where x < −2 all real values of x where −2 < x < 4 all real values of x where 1 < x < 4 all real values of x where x < 0
Answers
Answer:
c
Step-by-step explanation:
all real values of x where 1 < x < 4
Answer:
c
Step-by-step explanation:
trust me
8x^{3}+26x^{2}+19x+38x
3
+26x
2
+19x+3 is divided by 4x+34x+3.
Answers
Applying synthetic division, the quotient between 8x³ + 26x² + 19x + 3 by 4x + 3 is:
2x² + 5x + 1.
Synthetic division algorithmIn the synthetic division algorithm, the coefficients of a polynomial are each divided by a value.This divisor is the zero of the divided polynomial, which goes into the far left box.In this context of this problem, the coefficients of the polynomial 8x³ + 26x² + 19x + 3 are given as follows:
8, 26, 19 and 3.
The divisor is found as follows:
4x + 3 = 0
4x = -3
x = -3/4
x = -0.75.
The resulting coefficients of the quotient are given as follows:
8, 20, 4 and remainder of 0.
Hence the quotient is:
8x² + 20x + 4.
Which can be simplified as:
2x² + 5x + 1.
The first coefficient of the polynomial, of 8, was moved down, the multiplied by -0.75 and added to 26, resulting in 20. Then the same procedure was done with 20(multiplied with -0.75 and added with the next coefficient of 19), until the last coefficient of 3.
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13. Write an equation of the line that passes through (2/3, 1) and has a slope of -3.
a) Y = -3x + 3
b) Y = -2x - 1
c) Y = x - 1
d) Y = x + 3
Answers
Answer:
A
Step-by-step explanation:
A, is the only answer with the correct slope, and when you plug the coordinates in, you get 1=1
Will give Brainliest if right
Answers
The value of x is 14 and the value of y is 7√3.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
We know sin is opposite/hypotenuse
∴ sin30° = 7/x.
1/2 = 7/x.
x = 14.
We also know that tan is opposite/adjacent.
tan30° = 7/y.
1/√3 = 7/y.
y = 7√3.
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in a photograph, Dan is 2.5 inches tall and his sister Emma is 1.5 inches tall. don's actual height is 70 inches. what is Emma's height?
Answers
Emma's actual height is found to be 42 inches.
Explain about the proportion of number?The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The connection is proportional if the ratio remains constant. The association is not proportional if the ratio shifts.For the given question:
In a photograph,
Dan is 2.5 inches tall and his sister Emma is 1.5 inches tall.Dan's actual height is 70 inchesLet 'x' be the actual height of Emma.
Thus,
2.5 / 1.5 = 70 / x
x = 70*1.5 / 2.5
x = 42
Thus, Emma's actual height is found to be 42 inches.
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Can anyone Help me on this ?
Answers
Answer: 52=y and 15=x
Step-by-step explanation:
Since we know m and n are parallel that means alternate exterior angles are equal to each other.
The angle with 8x+8= the angle above the one that says 3x+7
Two angles on a line add up to 180 so 8x+8+3x+7=180
Now we can solve
\(8x+8+3x+7=180\\(8x+3x)+(8+7)=180\\11x+15=180\\11x+15-15=180-15\\11x=165\\\frac{11x}{11} =\frac{165}{11} \\x=15\)
Now we know that x=15
The angle y and the angle of 3x+7 are corresponding angles. Corresponding angles are congruent. Subbing in 15 for x we can solve for y
\(3(15)+7=y\\45+7=y\\52=y\)
If a food item with an original (AP) weight of 4 pounds at a cost of $1.10 per pound yields a servable weight of 2 pounds, what is the cost per servable pound for this food item? a. $0.50 b. $1.50 c. $2.20 d. $4.40
Answers
Given that the cost is $1.10 per pound, we can calculate the cost per servable pound by dividing the total cost ($1.10 * 4 pounds) by the servable weight (2 pounds). Therefore, the correct option is c. $2.20.
The original weight of the food item is 4 pounds, and the cost per pound is $1.10. Therefore, the total cost of the food item is 4 pounds * $1.10 = $4.40.
The servable weight of the food item is 2 pounds. To find the cost per servable pound, we divide the total cost ($4.40) by the servable weight (2 pounds):
Cost per servable pound = Total cost / Servable weight = $4.40 / 2 pounds = $2.20.
Hence, the cost per servable pound for this food item is $2.20. Therefore, the correct option is c. $2.20.
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(q13) Evaluate the definite integral.
Answers
The definite integral in this problem has the value given as follows:
B. 42.
How to solve the definite integral?The definite integral in the context of this problem is given as follows:
\(\int_0^2 (x^7 + 5) dx\)
Applying the power of x integral rule, the result of the integral is given as follows:
\(\frac{x^8}{8} + 5x\)
At x = 2, the numeric value of the integral is given as follows:
\(\frac{2^8}{8} + 5(2) = 42\)
At x = 0, the numeric value of the integral is given as follows:
0.
(as both terms involve a multiplication by x and x = 0).
Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:
42 - 0 = 42.
Hence option B is the correct option in the context of this problem.
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WILL MARK BRAINLIEST JUST PLZ PLZ HELP
Answers
Answer:
is this from a text book
Step-by-step explanation:
What is the arc length S what is shown below?
The angle in the image is a central angle în radians.
Answers
Answer:
14 cm
Step-by-step explanation:
The applicable formula is ...
s = rθ
s = (7 cm)(2) = 14 cm
Which expression is equivalent to startfraction 5 y cubed over (5 y) superscript negative 2 baseline endfraction?
Answers
The expression that is equivalent to the given expression is 125y⁵.
The given expression is:
\(\frac{5y^{3} }{(5y)^{-2} }\)
What are some important power rules applicable to the given problem?Some important power rules applicable to this problem are:
1)\((ab)^m=a^mb^m\)
2)\(\frac{1}{a^{-n} } =a^n\)
So, \(\frac{5y^{3} }{(5y)^{-2} } =\frac{5y^{3} }{5^{-2} y^{-2} }\).....by power rule (1)
\(=(\frac{5}{5^{-2} } )(\frac{y^3}{y^{-2} })\)
\(=5^3y^5\).....by power rule(2)
\(=125y^5\)
Hence, the expression that is equivalent to the given expression is 125y⁵.
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the ice cream above is going to melt
when it does, will it fit in the cone or will it overflow? explain
PLEASE HELP!
the spherical ice cream scoop and the
right cone have a radius of 3cm
the height of the cone is 7cm
show all your work
Answers
Since the volume of the sphere V = 36π cm³is greater than that of the cone, V' = 21π cm³ the ice cream will overflow.
What is the volume of a sphere?The volume of a sphere is given by V = 4πr³/3 where r = radius of sphere
Now if the ice cream above is going to melt when it does, will it fit in the cone or will it overflow? Since the ice cream is a sphere, the ice cream will not overflow if the volume of the ice cream equals the volume of the cone. If is greater than the volume of the cone, it will overflow.
Now, since the ice cream is a sphere, its volume is given by V = 4πr³/3 where r = radius of sphere = 3 cm
So, substituting this into the equation, we have that
V = 4πr³/3
V = 4π(3 cm)³/3
V = 4π × 27 cm³/3
= 4π × 9 cm³
= 36π cm³
Also, since the volume of the cone is given by V' = 1/3πr²h where r = radius of cone = 3 cm and h = height of cone = 7 cm
So, substituting the value of the variables into the equation, we have that
V' = 1/3πr²h
V' = 1/3π(3 cm)² × 7 cm
= 1/3π × 9 cm² × 7 cm
= 3π cm² × 7 cm
= 21π cm³
We see that V = 36π cm³ > V' = 21π cm³
Since the volume of the sphere is greater than that of the cone, the ice cream will overflow.
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A rectangles perimeter and its area have the same numerical value. The width of the rectangle is 10. What is the length of the rectangle? (Answer as a decimal.)
Answers
Answer:
The length of the rectangle, L = 2.5 units
Step-by-step explanation:
Given the following data;
Length of rectangle =?
Width of rectangle = 10 units.
Note:
The formula for calculating the perimeter of a rectangle is;
\(P = 2L + 2W\) ........equation 1
Substituting into equation 1, we have;
P = 2L + 2(10)
P = 2L + 20
The formula for calculating the area of a rectangle is given by;
\(A = L * W\) ..........equation 2
Substituting into equation 2, we have;
A = 10L
Since, the perimeter of the rectangle is equal to its area;
Perimeter = Area
2L + 20 = 10L
20 = 8L
L = 20/8
L = 2.5 units.
Find the coordinates of the midpoint of AB by finding the averages of the coordinates
1. A(4,3) B(8,8)
2. A(7,2) B(1,5)
3. A(-5,6) B(1,-3)
4. A(-7,-1) B(-5,-9)
Answers
#1
\(\\ \sf\longmapsto \left(\dfrac{4+8}{2},\dfrac{3+8}{2}\right)\)
\(\\ \sf\longmapsto \left(\dfrac{12}{2},\dfrac{11}{2}\right)\)
\(\\ \sf\longmapsto \left(6,\dfrac{11}{2}\right)\)
#2
\(\\ \sf\longmapsto \left(\dfrac{7+1}{2},\dfrac{2+5}{2}\right)\)
\(\\ \sf\longmapsto \left(\dfrac{8}{2},\dfrac{7}{2}\right)\)
\(\\ \sf\longmapsto \left(4,\dfrac{7}{2}\right)\)
#3
\(\\ \sf\longmapsto \left(\dfrac{-5+1}{2},\dfrac{6-3}{2}\right)\)
\(\\ \sf\longmapsto \left(\dfrac{-4}{2},\dfrac{3}{2}\right)\)
\(\\ \sf\longmapsto \left(-2,\dfrac{3}{2}\right)\)
#4
\(\\ \sf\longmapsto \left(\dfrac{-7-5}{2},\dfrac{-1-9}{2}\right)\)
\(\\ \sf\longmapsto \left(\dfrac{-12}{2},\dfrac{-10}{2}\right)\)
\(\\ \sf\longmapsto \left(-6,{-5}\right)\)
i realllllllllllllllllllllly neeeeeeddddd help on this one pleaseeeeeeeeeeeeeeeeeeeeee
Carlos traveled at an average speed of 70 miles per hour for 2.5 hours and then traveled at an average speed of 80 miles per hour for 3.5 hours. What was the total distance in miles that Carlos traveled during that time
Answers
Answer:
70 * 2.5 = 175
80 * 3.5 = 280
175 + 280 = 455 miles all together
Step-by-step explanation:
I hope this helps :)
Molly is painting her bedroom walls, and the paint costs $24 per gallon. How much does the paint cost per quart? $3 per quart $6 per quart $48 per quart $96 per quart
A: $3 per quart
B: $6 per quart
C: $48 per quart
D: $96 per quart
Answers
Answer:
the answer is B $6 per quart
Garry is studying a square pyramid and wants to draw a net of the figure to help determine its surface area. Which net represents a square pyramid?
Answers
The correct net that represents a Square pyramid is Option B.
A net is a two-dimensional pattern that can be folded into a three-dimensional figure. To draw a net of a square pyramid, we need to create a two-dimensional pattern that includes a square base and four triangular faces that meet at a common vertex.
Option A: This net has a square base, but it has three triangular faces and one trapezoidal face. Therefore, it does not represent a square pyramid.
Option B: This net has a square base and four triangular faces that meet at a common vertex. Therefore, it represents a square pyramid.
Option C: This net has a triangular base, so it does not represent a square pyramid.
Option D: This net has a square base, but it has six triangular faces that do not meet at a common vertex. Therefore, it does not represent a square pyramid.
Therefore, the correct net that represents a square pyramid is Option B.
It's important to note that there may be different ways to draw a net for a square pyramid, as long as the net includes a square base and four triangular faces that meet at a common vertex. However, Option B is a valid net for a square pyramid and represents the figure accurately.
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PLEASE HELP ILL GIVE BRAINLIEST!
Answers
The proportional relationship between the cost and the weight is c = 2.2w.
What is a proportional relationship?A proportional relationship is used to show the constant od proportionality between the variables.
One bag weighs 2.4 pounds and costs $5.28. The constant will be:
= 5.28/2.4
= 2.2
This can be expressed as c = 2.2w
where c = cost
w = weight
This shows the relationship.
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how many whole weeks are in a year
Answers
Answer:
52 weeks are there in a year
Step-by-step explanation:
365/7
Valerie is a member of a movie club. She pays a fixed fee of $40 annually. She must pay $6 for every movie she rents. She rented 14 movies this year. What is the total amount that she paid this year
Answers
Valerie paid a total amount of $124 this year for her movie club membership and the 14 movies she rented.
What is total amount?In math, the total amount typically refers to the final sum or result of a calculation involving multiple numbers or quantities.
Valerie pays a fixed fee of $40 annually, and she rented 14 movies at a cost of $6 each. Thus, the total amount she paid this year can be calculated as follows:
Total cost of movie rentals = 14 x $6 = $84
Adding the fixed annual fee to the rental costs:
Total amount paid by Valerie this year = $40 + $84 = $124
Therefore, Valerie paid a total of $124 this year for her movie club membership and the 14 movies she rented.
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Please help! will give brainlest!
Answers
cscθ is the same as 1/sinθ
Explanation:
csc stands for cosec which is equivalent to 1/sinθ
The expression is thus equal to 1/[sin(4π/3)]
Since we know by consulting the unit circle that sin(4π/3) = - [(√3)/2]
we get the expression 1/[sin(4π/3)] = 1/(-√3/2)
which can be simplified to 1/(-√3/2) = 2/(-√3) = (-2√3)/3
What is the range of the function represented by these ordered pairs? (
{(-1, -3), (-2, 0), (-3,5), (1, -3), (2, 0), (3,5)}
Answers
Answer:
6
Step-by-step explanation:
smallest x value is -3
largest x value is 3
so distance between them is 6
3- (-3)=6
Answer:
Step-by-step explanation:
CHALLENGE:
Combine like terms:
3y + 4xy + x + 2y + 2xy + x + 10 + 1
Answers
Answer: 2x+6xy+5y+11
Step-by-step explanation: