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Reika [66]
2 years ago
14

Ana has won a lottery. She was offered two options to receive the award: She can either take it in five installments of $60,000

annually, starting from now; or she can take a lump-sum of $255,000 now. Assuming (a) interest at an annual rate of 5% compounded annually, or (b) interest at an annual rate of 6% compounded continuously, which option should she choose under the consideration of cash value only?
A) If the interest is at the annual rate of 5%, compounded annually, then the present value of the five installments is $______. B) If the interest is at the annual rate of 6%, compounded continuously, then the present value of the five installments is $______.
Mathematics
1 answer:
AleksandrR [38]2 years ago
5 0

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now.

<u>First, we determine the value of the 5 installments using a 5% annual compounded rate.</u>

We calculate the future value, and then the present value:

FV= {A*[(1+i)^n-1]}/i

A= annual payments

FV= {60,000*[(1.05^5) - 1]} / 0.05

FV= $331.537.88

PV= FV/(1+i)^n

PV= $259,768.60

At an annual rate of 5% compounded annually, she should choose the five installments instead of the $255,000.

<u>Now, if the annual rate is 6% continuously compounded.</u>

<u>First, we need to calculate the effective interest rate:</u>

r= e^i - 1

r= effective inerest rate

r= e^0.06 - 1

r= 0.0618

FV= {60,000*[(1.0618^5) - 1]} / 0.0618

FV= 339,443.23

PV= 339,443.23/1.0618^5

PV= $251,509.01

At an annual rate of 6% compounded continuously, she should choose the $255,000.

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Answer:

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iragen [17]

Answer:

The image is (-18,0)

Step-by-step explanation:

Here, we want to find the image of the given point after dilation by the given scale factor

Mathematically, given a point with the pre-image (x,y) going under the dilation of scale factor k, centered at the origin, the coordinates of the image will be;

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Applying this in the given scenario, we have

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2 years ago
Zara translates figure p to make figure q. If she translates figure q 4 units to right to make figure r where will figure r be l
Morgarella [4.7K]

Using translation concepts, considering the vertices (x,y) of figure p, the following rule is applied to find the vertices of figure r.

(x,y) -> (x + 4, y).

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

When a figure is shifted 4 units to the right, <u>4 is added to the x-coordinate</u>, hence, considering the vertices (x,y) of figure p, the following rule is applied to find the vertices of figure r.

(x,y) -> (x + 4, y).

More can be learned about translation concepts at brainly.com/question/28416763

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1 year ago
Select the correct answer.
makvit [3.9K]

Answer:

<h3>64°</h3>

Step-by-step explanation:

y = 52° ( Opposite Angles )

y + 2x = 180° ( Interior Angles )

y + 2x =  {180}^{o}  \\  {52}^{o}  + 2x =  {180}^{o}  \\ 2x =  {180}^{o}  -  {52}^{o}  \\ 2x =  {128}^{o}  \\ x =  \frac{ {128}^{o} }{2} \\ x =  {64}^{o}  \\

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Answer:

i dont know what it means but the right image is 4 times larger than the left image

Step-by-step explanation:

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