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3 years ago

Charlie wants to make a one-time investment in an account that earns 4% interest compounded quarterly. To earn $315,930 after 21

Mathematics

1 answer:

KIM [24]3 years ago

8 0

Answer:

B. $136,960.54

Step-by-step explanation:

Rate = r = 4%

Times = b = 4

Future Value = A = $315,930

No. pf Years = n = 21

Present Value = P = ?

A = P [1 + (r / b)]ⁿᵇ

$315,930 = P [1 + (0.04 / 4]²¹ ˣ ⁴

$315,930 = P [1 + 0.01]⁸⁴

$315,930 = P [1.01]⁸⁴

$315,930 = P x 2.306723

P = $315,930 / 2.306723

P = $136,960.54

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A square garden is surrounded by a walkway of width X. If the area of the garden is 484 ft2 and the area covered by both the gar

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The width of the walkway is 3 feet, If the area of the garden is 484 $feet^{2}$ and the area covered by both the garden and the walkway (the entire square) is 784 $feet^{2}$ .

Step-by-step explanation:

The given is,

Area of the garden is 484 $feet^{2}$

Area covered by both the garden and the walkway (the entire square) is 784 $feet^{2}$ .

Let, x - Width of the walkway

Step:1

Formula to calculate area of square is,

$A= a^{2}$ ...........................(1)

Where, r - Radius of square

Step:2

For garden,

A = 484 $feet^{2}$

Equation (1) becomes,

$484=a^{2}$

Take square root on both sides,

$a=\sqrt{484}$

a = 22 feet

For garden and the walkway (the entire square),

A = 784 $feet^{2}$

Equation (1) becomes,

$784=a^{2}$

Take square root on both sides,

$a=\sqrt{784}$

a = 28 feet

Step:3

Ref attachment,

Side of garden and the walkway =

Side of garden + 2 (width of the walkaway)....(1)

28 = 22 + 2 ( x )

2 ( x ) = 28 - 22

= 6

$x = \frac{6}{2}$

Width, x = 3 feet

Result:

The width of the walkway is 3 feet, If the area of the garden is 484 $feet^{2}$ and the area covered by both the garden and the walkway (the entire square) is 784 $feet^{2}$ .