All categories

2 years ago

What is the present value of $3,000 per year for 9 years discounted back to the present at 10 percent?

Mathematics

1 answer:

Studentka2010 [4]2 years ago

3 0

Answer:

$17,277.07

Step-by-step explanation:

Present value of annuity is the present worth of cash flow that is to be received in the future, if future value is known, rate of interest is r and time is n then PV of annuity is

PV of annuity = $\frac{P[1-(1+r)^{-n}]}{r}$

= $\frac{3000[1-(1+0.10)^{-9}]}{0.10}$

= $\frac{3000[1-(1.10)^{-9}]}{0.10}$

= $\frac{3000[1-0.4240976184]}{0.10}$

= $\frac{3000(0.5759023816)}{0.10}$

= $\frac{1,727.7071448}{0.10}$

= 17,277.071448 ≈ $17,277.07

You might be interested in

I need answers to this

ololo11 [35]

Answer:

x = -5, and y = -6

Step-by-step explanation:

Suppose that we have two equations:

A = B

and

C = D

combining the equations means that we will do:

First we multiply both whole equations by constants:

k*(A = B) ---> k*A = k*B

j*(C = D) ----> j*C = j*D

And then we "add" them:

k*A + j*C = k*B + j*D

Now we have the equations:

-x - y = 11

4*x - 5*y = 10

We want to add them in a given form that one of the variables cancels, so we can solve it for the other variable.

Then we can take the first equation:

-x - y = 11

and multiply both sides by 4.

4*(-x - y = 11)

Then we get:

4*(-x - y) = 4*11

-4*x - 4*y = 44

Now we have the two equations:

-4*x - 4*y = 44

4*x - 5*y = 10

(here we can think that we multiplied the second equation by 1, then we have k = 4, and j = 1)

If we add them, we get:

(-4*x - 4*y) + (4*x - 5*y) = 10 + 44

-4*x - 4*y + 4*x - 5*y = 54

-9*y = 54

So we combined the equations and now ended with an equation that is really easy to solve for y.

y = 54/-9 = -6

Now that we know the value of y, we can simply replace it in one of the two equations to get the value of x.

-x - y = 11

-x - (-6) = 11

-x + 6 = 11

-x = 11 -6 = 5

-x = 5

x = -5

Then:

x = -5, and y = -6

5 0

3 years ago

Write down a fraction whose value lies between 3 and 4; whose denominator is a multiple of 5; whose numerator is a multiple of 1

slamgirl [31]

Answer:

33/10 and 55/15

Step-by-step explanation:

Possible denominators that are multiples of 5 less than 17 are 5, 10, 15.

Corresponding numerator ranges are [15, 20], [30, 40], and [45, 60]. In only two of these ranges are there any multiples of 11.

33 in [30, 40]

55 in [45, 60]

So, there are only two possible fractions meeting your requirement:

33/10 and 55/15

6 0

3 years ago

omar will donate up to $500 to charity. the money will be divided between two charities: the city of youth fund and educational

marshall27 [118]

Answer:

Please refer to the attached graph

Step-by-step explanation:

Knowing the following:

X = amount of money donated to the city youth fund

Y = amount of money donated to the educational growth foundation

We can write the statements in form of equations:

"Will donate up to $500, the money will be divided between two charities"

(a) $X + Y = \$ 500$

"The amount donated to the educational growth foundation to be at least four times the amount donated to the city youth fund"

(b) $Y \geq 4X$

If we graph both equations we can see the area where both conditions are met (see graph attached)

Where the blue line is (a) and the red line is (b)

Shaded area represent all the possible solutions for the donations, for example:

X=100 and Y=400 or

X=50 and Y=200, etc.

6 0

2 years ago

A triangle has ∠A, ∠B, and ∠C. ∠B is 20° more than ∠A. ∠C is double ∠B. How big is ∠A?

san4es73 [151]

Answer:

30°

Step-by-step explanation:

∠A + ∠B + ∠C = 180

∠B = ∠A + 20

∠C = 2 * ∠B

<A + (∠A + 20) + (2 * ∠B) = 180

<A + (∠A + 20) + (2 * (∠A + 20)) = 180

<A + (∠A + 20) + 2∠A + 40 = 180

4∠A + 60 = 180

4∠A = 120

∠A = 30

5 0

3 years ago

Read 2 more answers

During halftime of a soccer game, a slingshot launches T-shirts at the crowd. A T-shirt is launched from a height of 5 feet with

4vir4ik [10]

Hi,

During halftime of a soccer game, a slingshot launches T-shirts at the crowd. A T-shirt is launched from a height of 5 feet with an initial upward velocity of 72 ft. Per second. The T-shirt is caught 34 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time.

Write the general equation that represents height of the t-shirt as a function of time.

f(t) = -16 $t^{2}$ + 72t + 5

2. What is the maximum height of the t-shirt?

$t = \frac{-72}{2(-16)} = 2,25$ $f(2,25) = -16(2,25)^{2} + 72(2,25) + 5$

$= 86 feet$

1. How long will it take the t-shirt to reach its maximum height?

2,25 secondes

3. The range describes which values of the graph? What would the range of this graph be? (Write in inequality and interval notation).

height (y)

5 ≤ y ≤ 86 [ 5,86 ]

7 0

2 years ago

What is the present value of ​$3,000 per year for 9 years discounted back to the present at 10 ​percent?

What is the present value of $3,000 per year for 9 years discounted back to the present at 10 percent?