A debt of $3500 due in four years and $5000 due in six years is to be repaid by a single payment of $1500 now and three equal payments that are due each consecutive year from now. If the interest rate is 7% compounded annually, how much are each of the equal payments?

Answers

Answer 1

Answer:

$1715.44

Step-by-step explanation:

The formula to calculate the present value is;

PV = S(1 + r)^(-n)

Where;

S is the current debt

r is the interest rate

n is the amount of years which the debt is due.

Thus, for the debt of $3500 & $5000, we have total debt value as;

PV = (3500(1 + 0.07)^(-4)) + (5000(1 + 0.07)^(-6))

PV_debt = $6001.84

Now,let's find total PV of the payments that will be made since a single payment of $1500 now and three equal payments that are due each consecutive year from now annually;

PV_payments = 1500 + x(1 + 0.07)^(-1)) + x(1 + 0.07)^(-2)) + x(1 + 0.07)^(-3))

Where x is the value of each of the equal payments.

Thus, expanding we have;

PV_payments = 1500 + x(1.07)^(-1)) + x(1.07)^(-2)) + x(1.07)^(-3))

>> PV_payments = 1500 + x((1.07)^(-1)) + (1.07)^(-2)) + (1.07)^(-3))

Solving the bracket we have;

PV_payments = 1500 + 2.6243x

To find the value of each equal payments, we will equate PV_debt to PV_payments to get;

6001.84 = 1500 + 2.6243x

Thus;

2.6243x = 6001.84 - 1500

2.6243x = 4501.84

x = 4501.84/2.6243

x = $1715.44


Related Questions

PLS HELP MULTPLE CHOICE

Answers

Answer:

(-2,-1)

Step-by-step explanation:

Shoppers at a mall have a mean weight of 70 kg 70kg70, start text, k, g, end text with a standard deviation of 10 kg 10kg10, start text, k, g, end text. An elevator at the mall holds a maximum of 6 66 people, and safety engineers are curious about the average weight of shoppers on a full elevator. Suppose that we take random samples of 6 66 shoppers and calculate the mean weight x ˉ x ˉ x, with, \bar, on top of the shoppers in each sample.

Answers

Answer:

The answer is below

Step-by-step explanation:

Shoppers at a mall have a mean weight of 70 kg with a standard deviation of 10 kg. An elevator at the mall holds a maximum of 6 people, and safety engineers are curious about the average weight of shoppers on a full elevator. Suppose that we take random samples of 6 shoppers and calculate the mean weight x ˉ  on top of the shoppers in each sample.

Solution:

Let variable x represent the weight of a shopper at the mall.

Assuming this variable has a normal distribution with mean μ= 70kg and standard deviation σ = 10kg.  

There are random samples of 6 shoppers. That is sample size (n) = 6  

The mean of the sample (μₓ) is the same as the mean of the population (μ), hence:

μₓ = μ = 70 kg

The standard deviation of the sample (σₓ) is equal to the standard deviation of the population (σ) divided by the square root of the sample size (n).. Hence:

σₓ = σ / √n = 10 / √6 = 4.08 kg

Answer:

Mean: 70

Standard Deviation: 4.1

Step-by-step explanation:

Khan Academy Answer

Which is the graph of y = -(x - 3)2 - 1?
O
6-
у
|
5-
31
2+
1
« Previous

Answers

Answer:

Step-by-step explanation:

y = -½(x-3)²-1

This is the equation of a vertical parabola with vertex at (3,-1). The leading coefficient is negative, so the parabola opens downwards.

Which equation can be used to solve for x in the following diagram?
(10x + 10)
110°
Choose 1 answer:
(10x + 10)
= 110
(10x + 10) = 90
(10x + 10) - 110 = 90
(10x + 10) + 110 = 180

Answers

Answer:

the answers (10x+10)=110

Step-by-step explanation:

I need help please help

Answers

The answer is y=3x+26

What is the volume of a pyramid with a base area of 102 square units and a height of 13 units? 1) 442 units 2) 663 units 3) 1326 units 4) 3978 units.​

Answers

Answer:

3

Step-by-step explanation:

HOPE THIS HELPS SORRY FOR CAPS

Find the discriminant.
r2-6r+8=0
How many real solutions does the equation have?
no real solutions
one real solution
two real solution

Answers

In order to find the discriminant:
b^2-4ac

A= 1, B= 6, C=8

(6)^2-4(1)(8) = 4

Therefore, the equation has one real solution

Hari's weekly allowance varies depending on the number of chores he does. He received $18 in allowance the week he did 10 chores, and $16 in allowance the week he did 6 chores. Write an equation for his allowance in slope-intercept form.

Answers

Answer:

y=1/2x+13

Step-by-step explanation:

The slope-intercept form is: y=mx+b, where m is the slope and b is the y-intercept of the line. First, you have to calculate the slope using the following formula:

m=y2-y1/x2-x1

You have two points:  (6, 16), (10,18) as the chores are the independent variable which is x, and the money is the dependent variable which is y.

Now, you can replace the values in the formula:

y2=18

y1=16

x2=10

x1=6

m=(18-16)/(10-6)

m=2/4

m=1/2

Now, you use the point-slope formula:

y-y1=m(x-x1)

You have to replace the value of the slope and one point and solve for y:

y-16=1/2(x-6)

y-16=1/2x-3

y=1/2x-3+16

y=1/2x+13

According to this, the answer is that the equation for his allowance in slope-intercept form is: y=1/2x+13.

What fraction of the shape is shaded? plssss help

Answers

Answer:

2/6

Step-by-step explanation:

Answer:

1 1/2 of the shape is shaded

Step-by-step explanation:

Hope this helps!

wrote a simplified expression for the perimeter of the triangle
pls help i’ll give brainialist

Answers

Answer:

here, you are simply asked to find perimeter

so add all sides to find it. soln is below

a+5+2a-1+3a-7 = 6a-3= 3(2a-1) ans

I don’t know how to do this....Help me please!!

Answers

hahaha s cnxmskxxbzbd xbzbxbxbxnx
the picture is a black screen, we cannot help you,


Jessica weighs 10 less than three times as much as her little sister. If x represents her sister's weight, what is an expression Jessica can
use to figure out her own weight? Explain your thinking and how you got your answer.

Answers

Answer:

Step-by-step explanation:

J=3x-10

We are told Jessica weighs 10 less than 3 times her sister’s weight and told that her sister’s weight was x.

For Halloween Debby and her sister combined the candy they received. Debby had 32 pieces of candy while her sister had 45. If they ate 24 pieces the first night, how many pieces do they have left?

Answers

32+45-24=53 pieces they have left

What set of numbers does NOT contain -7?
o integers
rational numbers
real numbers
whole numbers

Answers

whole numbers
hi! .....

Answer:

Step-by-step explanation:

the answer is whole number, explination : A whole number is any number that does not contain a fraction, decimal, or negative value. For example, 1, 25, and 365 are whole numbers

Find the curcumince of the circle. use 3.14 or 22/7.​

Answers

Answer:

the circumference of this circle is approximately 25.12 cm with π as 3.14.

Step-by-step explanation:

circumference of a circle is technically a perimeter of a circle.

we find the circumference of a circle by using the following formula :

c = 2πr                                   or                                 c = πd

r represents the radius                                             d represents the diameter

since 4 yds here is a radius, we use the left formula i placed above. then, we substitute the numbers in. pi represents 3.14 as said in your question. even if you use 22/7, you will still get around the same result.

c = 2πr

c = 2(3.14)4

c = 6.28(4)

c = 25.12 yds

therefore, the circumference of this circle is approximately 25.12 yds.

A piece of rural land sold ten years ago for 40000. The price for the same land this year is $800 more per acre, and it sold for 60000. What is the size of the piece of land in acres?

Answers

Answer: 25

Step-by-step explanation:

From the question, we are informed that the piece of rural land sold ten years ago for 40000 and that the price for the same land this year is $800 more per acre, and it sold for 60000.

The size of the piece of land in acres will then be:

40000 + 800x = 60000

800x = 60000 - 40000

800x = 20000

x = 20000/800

x = 25

The land is 25 acres

Answer: 25

Step-by-step explanation:

40000 + 800x = 60000800x = 60000 - 40000800x = 20000x = 20000/800x = 25

On a snowy winters eve two candles are lit at the exact same time. A 18-inch candle and a 21-inch candle are lit at the exact same time. The 18-inch candle burns 2 inches every hour. The 21-inch candle burns 3 inches every hour. Create a system of equations using the information

Answers

Answer:

y=21-3x  and y=18-2x

Step-by-step explanation:

Ok, so we have candle A, which is 21 inches and burns 3 inches every hour. in slope-intercept form, the hours would be the x, the 21 is our y intercept. So the first equatio would be y=-3x+21 (negative slope, because the height of the candle is going down). Candle b, which is 18 inches, burns away 2 inches each hour. We can make -2 the slope (negative 2, since the candle is  being burned away, not being added to), and the 18 our y intercept. So the two equations would be

y=21-3x

and

y=18-2x

hope this helps!

A therapist wanted to determine if yoga or meditation is better for relieving stress. The therapist recruited 100 of her high-stress patients. Fifty of them were randomly assigned to take weekly yoga classes and the other 50 were assigned weekly meditation classes. After one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress. The therapist wants to construct a 95% confidence interval for the difference in proportions of patients experiencing stress relief after yoga and after meditation. Are the conditions for inference met?

Yes, the conditions for inference are met.
No, the 10% condition is not met.
No, the randomness condition is not met.
No, the Large Counts Condition is not met.

Answers

Answer:

A. Yes, the conditions for inference are met.

Explanation:

100%

How to solve this maths problem?
Pls help​

Answers

Answer:

Step-by-step explanation:

(a) The length and breadth of the playground as measured by the surveyor are 20 m and 13 m respectively to nearest metre.

Since the actual length is x m and breadth is y m, then;

i.               x ≥ 20 m or x ≤ 20 m

ii.              y ≥ 13 m or y ≤ 13 m

(b) perimeter of the playground = 2 (length + breadth)

                                                     = 2 ( 20 + 13)

                                                     = 2 x 33

                                                     = 66 m

The range of values of the perimeter = 65.4 m < perimeter < 66.5 m

ii. area of the playground = length x breadth

                                          = 20 x 13

                                         = 260 [tex]m^{2}[/tex]

The range of values of the area = 259.4 [tex]m^{2}[/tex] < Area <  260.5 [tex]m^{2}[/tex]

Find the slope of the two points: (6,0) and
(4, -12).

Answers

Answer:

m=6

Step-by-step explanation:

the slope (m) of a line from two points is given as (y2-y1)/(x2-x1).

the points given are (6,0) and (4,-12)

we can label the points:

x1=6

y1=0

x2=4

y2=-12

now substitute into the equation

m=(-12-0)/(4-6)

subtract

m=-12/-2

divide

m=6

the slope is 6

hope this helps! :)

A system of two equal equations is shown below
3x + y = 8
4x - 2y = 3
What is the solution of the system?

Answers

Answer:

x=1.9

y=2.3

Step-by-step explanation:

I hope this helped.

Quadrilateral BCDE is inscribed in circle A. The measure of ⏜ is 73°. The measure of ⏜ is 53° and the measure of ⏜ is 102°. Determine the measure of ∠ BCD.

Answers

Answer: c

Step-by-step explanation:

Fill in the blank:
(2x + 3)(x + 1) = 2.2 + ___+3
A)-5
B)3
C)0
D)5

Answers

B bbbbbbbbbbbbbbbbbbbb(B)

Two 7th grade , Monique and Matt, both solved the following math problem.

If the temperature drops from 30*F to -5*F by how much did the temperature decrease?
The students came up with different answers.Monique said the answer is 35*F , And Matt said the answer is 25*F. Who is correct?

Answers

Answer:

Monique is correct

Step-by-step explanation:

The actually temperature decrease = 30 - (-5) = 35*F

Monique is correct

62% of the people in a cinema are children.
If there are 93 children in the cinema, calculate the total number of people in the
cinema.
You must show your calculations. *
2 Points)
Enter your answer

Answers

Answer:

143

Step-by-step explanation:

62/2=31

93/2=46.5

62%+31%=93%

93+46.5= 139.5

7-3=4

4% of 93= 3.72

139.5+3.72= 143.22

theres no such thing as 0.22 of a person so its 143

2a.) A(t) is the average high temperature in Aspen, Colorado, "t" months after the

start of the year. M(t) is the average high temperature in Minneapolis, Minnesota,

"t" months after the start of the year. Temperature is measured in degrees

Fahrenheit. Which function had the HIGHER average rate of change between the

beginning of January and middle of March? *

Answers

Answer:

As you didn't add the graph, I will for you.

Step-by-step explanation:

The correct answer is Minneapolis because as you can see Aspen did not change as dramatically as Minneapolis.

The start of January and the middle of March, Minneapolis, or function M(t), had a larger average rate of change. It means that Minneapolis experiences a greater increase in temperature than Aspen does.

What is meant by function?

A mathematical formula, rule, or legislation that establishes the link between the independent variable and the dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

In the beginning of January, Aspen's temperature was 35° F, and in the middle of March, it was 48° F. 3.5 months later Minneapolis has lows of 25 degrees Fahrenheit in January and highs of 50 degrees Fahrenheit in the middle of March (at 3.5 months).

So, the average rate of change of temperature of Aspen between the points (1, 35) and (3.5, 48) exists

[tex]$\frac{y_2-y 1}{x_2-x_1}=\frac{48-35}{3.5-1}=5.2$[/tex]

The average rate of change of temperature of Minneapolis between the points (1, 25) and (3.5, 50) is [tex]$\frac{50-25}{3.5-1}=10$[/tex]

Thus, from the start of January and the middle of March, Minneapolis, or function M(t), had a larger average rate of change. It means that Minneapolis experiences a greater increase in temperature than Aspen does.

To learn more about function refer to:

https://brainly.com/question/11624077

#SPJ2

Estimation on a scale drawing of a fence, 3.75 inches represent 24 feet . what. is the actual length of a second fence is 2.8 inches in the drawing?

The exact length of the second fence is __ feet. ​

Answers

Answer: 17.92 feet

Step-by-step explanation:

From the question, we are informed that the estimation on a scale drawing of a fence is that 3.75 inches = 24 feet.

Based on the above, 1 inch will be:

= 24/3.75

= 6.4 feet

Therefore, the actual length of a second fence that is 2.8 inches in the drawing will be:

= 6.4 × 2.8

= 17.92 feet

Rachel and Keegan are building a stand like the one shown to display framed photos. what is the surface area of the stand? length 7ft, width 1ft, height 2ft.

Answers

Answer:

it a because digkjg

Step-by-step explanation:

1 goes to 2 adnd it stops like that

What’s the missing term ?

Answers

Answer:

2x^2

Step-by-step explanation:

Your answer is 2x^2 (two x squared)
Deltamath stinkssss I felt that

Which points lie on a circle that has its center at the origin and contains the point (0, 3)?

Answers

Answer:

(1,2[tex]\sqrt{2}[/tex])

Other Questions
Read carefully and choose the name of the student who made the correct statement ..... HELPPP Which equation describes the sum of the two vectors plotted below?6O A. P = 8+ 4yB. f = +C. P = 38 - 27D. P = -8 - 4y Tamara is 7 years older than her sister. The sum of their age is 27.What is Tamara's age ? I need help figuring this problem out WILL GIVE BRAINLIEST Mya has $90 to spend. She wants to buy as many DVDs as possible after buying some CDs that costs $22. The DVDs cost $17 each at most. What is the greatest number of DVDs she can buy? If the company were to issue an annual zero-coupon bond with a maturity of 2 years and a par value of $1,000, what would be the arbitrage-free price of that bond? Please solve these system of equations using elimination. Random answers or links will be reported.1. 6x+2y=40 8x+3y=472. 6x+5y=34 6x+6y=273.8x+2y=646x+3y=344.5x+5y=268x+3y=365. 6x+3y=364x+5y=466. 2x+9y=418x+4y=36 What do Coronary artery and coronary veins connect the heart with Can any one solve it Someone mind helping? Awnsers:A. 8B.12C.16D. 20 Which of the following processes is endothermic?Any combustion reactionBonds being made in the productsBonds being broken in the reactants Balance the following chemical equationMg + O MgO What is the volume of a cylinder, in cubic centimeters, with a height of 15 centimetersand a base diameter of 6 centimeters? Round to the nearest tenths place A cuboid has side lengths 3cm, 4cm and 7cm. A cylinder with a height double that of the longest side of the cuboid has the same volume. Calculate the radius and the surface area of the cylinder. TFind the sum of (x2 7x + 5) and (-3x2 - x + 10)[ im giving you alot of points to check this over!! PLEASE HELP ASAP!!!A car is sitting on a hill which is 25 m higher than ground level. What is the mass of the car if it contains 360,800 J of potential energy? How do scientists plan on unlocking the secrets to Mars? plllzzzzz help its math :( ILL GIVE U BRAINLIST AND A THANK YOU AND PLUS U GET POINTS!! :)