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kirza4 [7]
3 years ago
9

Approximately how much principal would need to be placed into an account earning 3.575% interest compounded quarterly so that it

has an accumulated value of $68,000 at the end of 30 years?
a.
$23,706
b.
$23,377
c.
$52,069
d.
$58,944
Mathematics
2 answers:
Ainat [17]3 years ago
7 0

<u>Answer-</u>

<em>$23377</em><em> must be deposited to get $68000 at the end of 30 years.</em>

<u>Solution-</u>

We know that for compound interest,

A=P(1+\dfrac{r}{n})^{nt}

Where,

A = Future amount = $68,000

P = ??

r = 3.575% annual = 0.03575

n = 4 as interest is compounded quarterly

t = time in year = 30 years

Putting the values,

\Rightarrow 68000=P(1+\dfrac{0.03575}{4})^{4\times 30}

\Rightarrow 68000=P(1.0089375)^{120}

\Rightarrow P=\dfrac{68000}{(1.0089375)^{120}}

\Rightarrow P=23377.45

Therefore, $23377 must be deposited to get $68000 at the end of 30 years.



Vsevolod [243]3 years ago
3 0

Answer:

Option b- $23,377

Step-by-step explanation:

Given : An account earning 3.575% interest compounded quarterly so that it has an accumulated value of $68,000 at the end of 30 years.

To find : How much principal would need to be placed into an account?

Solution :

Using compound interest formula,

A=P(1+\dfrac{r}{n})^{nt}

Where,

A = Future amount = $68,000

P = Principal value =?

r = 3.575% annual = 0.03575

n = 4  (interest is compounded quarterly)

t = time in year = 30 years

Putting the values,

68000=P(1+\dfrac{0.03575}{4})^{4\times 30}

\Rightarrow 68000=P(1.0089375)^{120}

\Rightarrow P=\dfrac{68000}{(1.0089375)^{120}}

\Rightarrow P=23377.45

Therefore, $23,377 must be deposited to get $68000 at the end of 30 years.

Hence, Option b is correct.

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Viktor [21]

The bearing of the tree from Q is 296.565°

<h3>How to determine the height of the tree?</h3>

The figure that illustrates the bearing and the distance is added as an attachment

The given parameters are:

Base of the tree, b = 50 meters

Angle (x) = 32 degrees

Calculate the height (h) of the tree using:

tan(x) = height/base

So, we have:

tan(32°) = h/50

Make h the subject

h= 50 × tan(32°)

Evaluate

h = 31.24

Hence, the height of the tree is 31.24 meters

<h3>How to determine the distance between Q and the base of the tree?</h3>

The distance (d) between Q and the base of the tree

This is calculated using the following Pythagoras theorem

d = √(100² + 50²)

Evaluate

d = 111.80

Hence, the distance between Q and the base of the tree is 111.80 meters

<h3>How to determine the angle of elevation?</h3>

The angle of elevation (x) using the following tangent trigonometric ratio

tan(x) = h/d

This gives

tan(x) = 31.24/111.80

Evaluate the quotient

tan(x) = 0.2794

Take the arc tan of both sides

x = 15.61

<h3>The bearing of the tree from Q </h3>

This is calculated using:

Angle of bearing = 270 + arctan(50/100)

Evaluate the arc tan

Angle of bearing = 270 + 26.565

Evaluate the sum

Angle of bearing = 296.565

Hence, the bearing of the tree from Q is 296.565 degrees

Read more about bearings at:

brainly.com/question/24142612

#SPJ1

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