Ask question

Ask question

All categories

dimulka [17.4K]

2 years ago

5

What is the present value of a $50,000 decreasing perpetuity beginning in one year if the discount rate is 7% and the payments d

ecline by 4% annually?

1 answer:

Trava [24]2 years ago

4 0

Answer:

Present Value = $1666666.67

Step-by-step explanation:

Present Value of a Growing Perpuity is calculated using the following formula

PV =D/(r - g)

Where D = Dividend

r = Discount Rate

g = Growth rate

D = $50,000

r = 7%

r = 7/100

r = 0.07

g = 4%

g = 4/100

g = 0.04

PV = D/(r-g)

Becomes

PV = $50,000/(0.07-0.04)

PV = $50,000/0.03

PV = $1,666,666.67

So the Present Value of the perpuity is $1,666,666.67

You might be interested in

A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

den301095 [7]

Answer:

The maximum height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> the height of the prism

we know that

the area of the rectangular base of the prism is equal to

$A=L*W$

$A\leq 27\ m^{2}$

so

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Substitute equation B in equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substitute equation B and equation D in the inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The solution for x is the interval----------> $[0,12]$

see the attached figure

but remember that

The width of the base must be $9$ meters less than the height of the prism

so

the solution for x is the interval ------> $(9,12]$

The maximum height of the prism is $12\ m$

8 1

2 years ago

Read 2 more answers

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select t

tankabanditka [31]

Help me I’m on the test review and I don’t get it someone help stupid edgenuity teachers are too lazy to teach us themselves

4 0

2 years ago

Read 2 more answers

A teacher wants to see if a new unit on factoring is helping students learn. She has five randomly selected students take a pre-

sergiy2304 [10]

Answer:

The <em>t</em>-value used for the 95% confidence interval of paired data is 2.776.

Step-by-step explanation:

The confidence interval formula for mean difference for a paired data is as follows:

$CI=\bar x_{d}\pm t_{\alpha/2, (n-1)}\times \frac{s_{d}}{\sqrt{n}}$

Here,

$\bar x_{d}$ = sample mean of the difference,

$s_{d}$ = sample standard deviation of the difference,

<em>n </em>= sample size (both samples are of same size).

$t_{\alpha/2, (n-1)}$ = critical value of <em>t</em>

(<em>n</em> - 1) = degrees of freedom

The information provided is:

<em>n</em> = 5

Confidence level = 95%

The critical value of <em>t</em> is:

$t_{\alpha/2, (n-1)}=t_{0.05/2, (5-1)}$

$=t_{0.025, 4}$

$=2.776$

*Use a <em>t</em>-table for the critical value of <em>t</em>.

Thus, the <em>t</em>-value used for the 95% confidence interval of paired data is 2.776.

4 0

2 years ago

How close are a meter and a yard? Convert, 1 meter into yards by using the fact that there are 100 centimeters in a meter, 2.54

Sveta_85 [38]

Answer:

To convert 1 meter into yards

Using the given facts : 100 centimeters in a meter, 2.54 centimeters in an inch, 12 inches in a foot, and 3 feet in a yard.

we can write these as;

$1 m = 100 cm$

$1 inches = 2.54 cm$

$1 ft = 12 inches$ and

$1 yard = 3 ft$

1 ft = 12 inches

3 ft = $3 \times 12 = 36 inches$

Since,

1 inches = 2.54 cm

36 inches = 91.44 cm

Also,

1 m = 100 cm

or

1 cm = $\frac{1}{100} m$

then;

91.44 cm = $\frac{91.44}{100} =0.9144 m$

⇒ 1 yards = 0.9144 m

Divide both sides by 0.9144 we get;

1 meter = $\frac{1}{0.9144} = 1.0936133$ yards.

Therefore, the answer is, 1 m = 1.1 yards (nearest to tenth)

5 0

2 years ago

In which set do all of the values make the inequality 2x - 1 < 10 true?

igomit [66]

$2x - 1 < 10\Leftrightarrow 2x < 11\Leftrightarrow x < \frac{11}{2}$

8 0

2 years ago