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Lelu [443]
3 years ago
5

Explain which variables would be included when using technology to calculate the present value of a lump sum and to calculate th

e present vaule of an annuity
Mathematics
1 answer:
koban [17]3 years ago
8 0

Answer:

a. Present value of a lump sum =

PV = FV / ( 1 + i )ⁿ

b. Present value of an annuity =

P = PMT x ((1 – (1 / (1 + r)⁻ⁿ )) / r)

Step-by-step explanation:

a. Present Value of a Lump sum =

PV = FV / ( 1 + i )ⁿ

Where variables in the formula are explained as follows

PV = Present Value of the given amount today

FV = Future Value of the given amount

i = Discount rate

n = Number of periods

b. Present value of an annuity is given as:

P = PMT x ((1 – (1 / (1 + r)⁻ⁿ)) / r)

The variables in the equation are explained as the follows:

P = the present value of annuity

PMT = Payment per period or the amount in each annuity payment

r =  the interest or discount rate

n = total number of periods or the number of payments left to receive

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The ratio would look like 63:3.5, if simplified it would look like 18:1
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3 years ago
You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o
anyanavicka [17]

Answer:

x =\dfrac{45 \sqrt{6}}{ 2}

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}

In order to estimate the point along the shore, x meters from B, the runner should  stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

=\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0

-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0

\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}

\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}

\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}

\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}

squaring both sides; we get

\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}

\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}

By cross multiplying; we get

49x^2 = 25(54^2+x^2)

49x^2 = 25 \times 54^2+ 25x^2

49x^2-25x^2 = 25 \times 54^2

24x^2 = 25 \times 54^2

x^2 = \dfrac{25 \times 54^2}{24}

x =\sqrt{ \dfrac{25 \times 54^2}{24}}

x =\dfrac{5 \times 54}{\sqrt{24}}

x =\dfrac{270}{\sqrt{4 \times 6}}

x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}

x =\dfrac{45 \sqrt{6}}{ 2}

8 0
3 years ago
How is this number read? 14.102
qwelly [4]

Answer:

fourteen and one-hundred-two

Step-by-step explanation:

we tend to read "." as "point" but the proper reading would be to read the number left to the decimal point (14), add the word "and" and then read the number to the right of the decimal point (102)

5 0
2 years ago
Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the g
kati45 [8]

Answer:

Option: D is correct.

Step-by-step explanation:

since we are given a inequality as:

y

Clearly from the graph of the following inequality we could see that the origin is included in the shaded region and the shaded area is below the line.

Also it could be seen that if we put the origin points i.e. (0,0) in the inequality than 0<2 and the condition is true and hence origin is included in the shaded area.

Hence, option D is true.

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3 years ago
Out of a food critic, social worker, radio DJ, and a computer game designer which career would you most likely apply concepts fr
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A computer game designer.
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3 years ago
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