Mathematics College

Consider a lottery that pays to the winner an annuity of $500 that begins immediately (an annuity due) and then annually in year 1 through year 16 with one exception. Because of high administrative costs associated with running the lottery, the payment in year 11, and only 11, is not $500 but $0. Using an interest rate of 8%, determine the present value of this cash flow stream.

Answers

Answer 1

The present value of an annuity that pays $500 per year from year 1 - 16 is $4711.24

An annuity can be defined as the payment of a specified amount of money for a stated period.

Present value is the value of the discounted cash flows at time zero

Present value is the sum of the discounted cash flows from year 1 to 16

Present value in year 0 = $500

Present value in year 1 =  $500 / (1.08) = 462.96

Present value in year 2 = $500 / (1.08^2) = 428.67

Present value in year 3 = $500 / (1.08^3) =396.92

Present value in year 4 = $500 / (1.08^4) = 367.51

Present value in year 5 = $500 / (1.08^5) =340.29

Present value in year 6= $500 / (1.08^6) = 315.08

Present value in year 7 = $500 / (1.08^7) =291.45

Present value in year 8 = $500 / (1.08^8) = 270.13

Present value in year 9 = $500 / (1.08^9) = 250.12

Present value in year 10 = $500 / (1.08^10) = 231.60

Present value in year 11 = 0

Present value in year 12 = $500 / (1.08^12) =198.56

Present value in year 13 = $500 / (1.08^13) =183.85

Present value in year 14 = $500 / (1.08^14) =170.23

Present value in year 15 = $500 / (1.08^15) =157.62

Present value in year 16 = $500 / (1.08^16) =145.95

Sum of present values is $4711.24

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Related Questions

A house was sold for $60,000 ten years ago. It has increase in value 55%. What is the value of the house now?

Answers

93,000 ? i believe. tell me if i’m wrong.

Solve the system of linear equations.

Solve the system of linear equations.

Answers

Answer:

work is shown and pictured

Solve the system of linear equations.

determine the intersepts of the lines ​

determine the intersepts of the lines

Answers

Answer:

Y-intercept is (0, 100) and the X-intercept is (-250, 0)

Step-by-step explanation:

For the y-intercept the line from the origin does not move left or right and stays at 0 but it goes up by 100.

For the x-intercept the line does not go up and down but it goes to the left -250.

Mary had 60$ and spent 3/4 on a coat. plus she brought a skirt with 1/2 she had left . how much do she have left?

Answers

3/4 of $60 = $45 for the coat
60 - 45 = $15 left
1/2 of $15 = $7.50 for the skirt
15 - 7.50 = $7.50 left

Classify the triangles either by their sides or their angles. Explain how you know the classification for the triangles.

Classify the triangles either by their sides or their angles. Explain how you know the classification
Classify the triangles either by their sides or their angles. Explain how you know the classification

Answers

Answer: Scalene and isosceles

Step-by-step explanation:

A wallet contains 34 notes, all of which are either $5 or $10 notes. If it amounts to $235, how many $10 notes are there?

Answers

Let's assume that the number of $5 notes in the wallet is x, and the number of $10 notes is y.

According to the problem, we know that:

- x + y = 34 (since the wallet contains a total of 34 notes)
- 5x + 10y = 235 (since the total amount of money in the wallet is $235)

We can use the first equation to solve for x in terms of y:

x = 34 - y

Substituting this expression for x into the second equation, we get:

5(34 - y) + 10y = 235

Simplifying and solving for y, we get:

y = 15

Therefore, there are 15 $10 notes in the wallet.

Answer:

For this question, you can use the simultaneous equation to solve this problem.

Equation 1 reads: x + y = 34. (There are 34 notes in total.)

Equation 2: 5x + 10y = 235 (The notes are worth a total of $235.)

To find x in terms of y, we can apply equation 1:

x = 34 - y

When we use this expression to replace x in equation 2, we obtain:

5(34 - y) + 10y = 235

By condensing and figuring out y, we get at:

y = 15

There are 15 $10 bills in the wallet as a result.

Can someone help me solve multiple step equations? For example (7t - 2) - (-3t + 1) = -3(1 - 3t)

Answers

Answer:

t = 0

Step-by-step explanation:

(7t - 2) - (-3t + 1) = -3(1 - 3t)

because you can not do anything inside the parantheses, you distribute. there aren't any numbers on the left side of the parantheses on the left side of the equation so we just imagine the number 1. on the right side of the equation, just distribute normally

[ 1(7t - 2) -1(-3t + 1) = -3(1 - 3t) ]

will be

7t - 2 + 3t - 1 = -3 + 9t

add like terms

10t - 3 = -3 + 9t

subtract 9t from both sides

t - 3 = -3

add 3 to both sides

t = 0

Suppose m angle 6=85. Find m angle 4

Suppose m angle 6=85. Find m angle 4

Answers

Answer:

Hey there!

Angle 6 and 4 are alternate interior angles.

Thus, 4 is 5 degrees.

Let me know if this helps :)

Simplify 1/4 (8m - 4n) + 1/3 (6m + 3n).

Answers

Expand the brackets first
2m - n + 2m + n = 4m

Solve for all values of x:
√8x + 1 = √2x + 5

Answers

Step-by-step explanation:

\( \sqrt{8} x - \sqrt{2} x = 4\)

\(x( \sqrt{8} - \sqrt{2} ) = 4\)

\(x = \frac{4}{ \sqrt{8} - \sqrt{2} } \)

the second term could be positive or negative

therefore

x=2.83 or

=-2.83

which is the square root of 8 - and positive

Will give brainliestt

Will give brainliestt

Answers

Answer: (-5, -3)

Step-by-step explanation:

(-10, -6)

-10/2 = -5

-6/2 = -3

find the value of angle BAC​

find the value of angle BAC

Answers

Answer:

The value of angle BAC = 75°

Step-by-step explanation:

=> Angle BAC + 105° = 180°

=> Angle BAC = 180° - 105°

=> Angle BAC = 75°

Which story problem can be solved using the expression 5 divided by ¼?
Group of answer choices

1. Suzy needs 5 pieces of ribbon that are each ¼ yard long. What is the total length of the ribbon?

2.Sammy pours ¼ cup of honey equally into 5 teacups. How much honey does he pour into each teacup?

3.Nicole cuts 5 feet of string into ¼ - foot pieces. How many pieces does she cut?

4.Alex cuts ¼ of a pizza into 5 slices. What part of the pizza is one of the slices he cuts?

Answers

Answer:

3. Nicole’s problem

Step-by-step explanation:

when you cut strings into smaller pieces that is dividing

5/1/4

5*4

20 pieces

Hopes this helps please mark brainliest

Factor the following quadratic expression: -2x^2 + 4x +8

Answers

i think it’s -2(x^2 -2x -4)

C is equidistant to which of the following points

C is equidistant to which of the following points

Answers

The point C is equidistant to (b) CL = CM = CN

How to determine the equidistant points

From the question, we have the following parameters that can be used in our computation:

The triangle

From the triangle, we can see that the point C is the centroid of the triangle

As a general rule:

The centroid is the geometric centre of a triangle. It is equidistant from all the points present on the triangle.

This means that point C is equidistant from L, M and N

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There are 16 fruits on the table. Maria has
three more than trice fruits as Jack. Paul has
one less than thrice fruit as jack. How many
fruits does each person have?

Answers

Jack has 2, Maria has 9, Paul has 5.

Factor –6x^2 – x + 2

Plus checking with FOIL

Answers

Answer:

x= 1/2 or x= -2/3

Step-by-step explanation:

-6x²-x+2=0

-6x²-4x+3x+2=0

-2x(3x+2) + 1(3x+2)=0

(-2x+1) (3x+2)=0

-2x+1=0 or 3x+2=0

x= -1/-2 or x= -2/3

so therefore

x=1/2 0r -2/3

using FOIL method

FIRST: (-2x)(3x)= -6x²

OUTER: (-2x)(2)= -4x

INNER: (1)(3x)= 3x

LAST: (1)(2) =2

-6x²-4x+3x+2

Find the solutions of the quadratic equation 5x2- x+ 6 = 0.

Answers

The answer is

X= -2/3


please help meeeee 100 points!!!!!!!!!!!!!!

please help meeeee 100 points!!!!!!!!!!!!!!

Answers

Its 12.92 and this is only 5 points

Answer:

when you will give us 100 points we will be giving your answers okay dear

PLEASE HELP ME i need help

PLEASE HELP ME i need help

Answers

Answer:

C.

\( \sqrt{5x - 7} + 13\)

Step-by-step explanation:

When facing a problem like this think of the x in G(x) as the variable (which it essentialy is). So if you replace the x in G(x) with F(x) you get

\(g(f(x)) = \sqrt{f(x)} + 13\)

and if you substitute F(x):

\(g(f(x)) = \sqrt{f(x)} + 13 = \sqrt{5x - 7} + 13\)

What is the difference between 100 and 33?

Answers

Answer:

67

Step-by-step explanation:

100 - 33 = 67

The difference between 100 and 33 is 67.

The answer is 67 if you go to your calculator app and do 67+33 it equals 100

A quadratic equation, y = ax^2 - 6x + 10, has exactly one real root. Calculate the value of a.

Answers

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

1+2+9*8=



...................................

Answers

Answer:

75

Step-by-step explanation:

1+2=3

3+9=12

12*8=75

Answer:

easy 75

Step-by-step explanation:

Question 3(Multiple Choice Worth 3 points)
(01.04 LC)
Which of the following expressions is equivalent to 2x +4? (The x+4 is to the power of x)
A) 8(2) ^x
B) 2^x/8
C) 16(2)^x
D) 2^x/16

Question 3(Multiple Choice Worth 3 points)(01.04 LC)Which of the following expressions is equivalent

Answers

The expression that is equivalent to the expression 2ˣ⁺⁴ is 16(2ˣ)

Which expression is equivalent to the expression

From the question, we have the following parameters that can be used in our computation:

2ˣ⁺⁴

The above expression is an exponential expression with the following properties

Base = 2Exponent = x + 4

When the above expression is expanded, we have

2ˣ⁺⁴ = 2ˣ * 2⁴

Evaluate the expression 2 exponent 4

So, we have the following representation

2ˣ⁺⁴ = 2ˣ * 16

Rewrite as follows

2ˣ⁺⁴ = 16 * 2ˣ

This gives

2ˣ⁺⁴ = 16(2ˣ)

Hence, the expression that is equivalent to the expression is 16(2ˣ)

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3,4,4,5,5,5,5,7,7,8,810,10,10,14 5 numbers have a mean of 6, a median of 5 and a mode of 4. The largest number is 10. Find the numbers.

Answers

Answer:

Step-by-step explanation:

MODE

3,4,4,5,5,5,5,5,7,7,8,8,10,10,14

MEAN

10-6=4

MEDIAN

3,4,4,5,5,5,5,5,5,7,7,8,8,10,10,14 CROSS OUT THE FIRST AND THE END THE DO IT AGAIN UNTIL YOU GET TO THE middle.

MEDIAN =5

RANGE IS BIGGEST- SMALLEST

10-3=7  

helpp anyone?? :(
No linkssss porfavorr plaesaaje cjkq

helpp anyone?? :(No linkssss porfavorr plaesaaje cjkq

Answers

Answer:

127/100 = 1.27

1.4

1 whole and 1/3 = 1.5

Step-by-step explanation:

Hope this helps

May I get Braineist pls

what is the value of the expressions 3m+4n -18 when m=10 and n=0

Answers

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Substituting the values for the letters, we have

3(10) + 4(0) -18

30 + 0 - 18

30 - 18

= 12

An employee who earns $12/hour, worked 37 hours this week, is paid a commission of $40 for each sale, and makes 9 sales during the same week, has earned total commissions of $ .

Answers

The total commission that's earned will be $360.

How to illustrate the expression?

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, an employee who earns $12/hour, worked 37 hours this week, is paid a commission of $40 for each sale, and makes 9 sales during the same week. Employees receive commission, also referred to as a sales commission, based on the sales they generate. A sales commission is a payment made to an employee after they successfully complete a task, typically selling a predetermined volume of goods or services. Sales commissions are a common incentive used by employers to boost employee productivity. A commission can be paid instead of or in addition to a salary.

The total commissions will be:

= Amount of commission × Number of sales

= $40 × 9

= $360

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Consider the equation 7x+2(x+5)=9x+10.
(a) Show that x=-5 and x = 2 are both solutions to this equation.

Answers

Answer:

7*-5+2(-5+5)=-35

9*-5+10=-35

7*2+2(2+5)=28

9*2+10=28

Step-by-step explanation:

when plugging the x values in, you get the same answer for both equation, make the equation equal.

Guess what sport I do and I'll give you brainly :)

Answers

Answer:

Gymnastics

Step-by-step explanation:

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