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Vanyuwa [196]
3 years ago
8

An amount of 46,000 is borrowed for 9 years at 6.25% interest, compounded annually. If the loan is paid in full at the end of th

at period, how much must be paid back?
Use the calculator provided and round your answer to the nearest dollar.
Mathematics
1 answer:
o-na [289]3 years ago
5 0

Answer:

You must pay $79,381.3

Step-by-step explanation:

This is a problem of compound interest.

The formula used to solve these problems is:

P = p_0(1 + r) ^ t

Where P is the amount that must be paid at the end of t years,

p_0 is the initial amount

r is the compound interest rate

If the initial amount was 46,000

The compound interest rate is 0.0625 and the loan is for 9 years, then at the end of the 9 years, the amount that must be paid is:

P = 46,000(1 + 0.0625) ^ 9

We solve for P and obtain:

P = 79,381.3

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A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down t
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The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.

<h3>What is the area of a rectangle?</h3>

The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:

Area of a rectangle = length(x) × breath(y)

1000000 sq.ft = (x) × (y) ---- (1)

However, to determine the fencing, we have:

Length of fencing = 2x + 2y  

  • since the rectangle has four sides and opposite sides are equal

Suppose we use the x-direction to estimate the region where the fencing is located, we have:

Length of fencing = 2x + 2y + x

Length of fencing = 3x + 2y ---- (2)

From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)

The Length of fencing is:

\mathbf{L = 3x - 2( \dfrac{1000000}{x})}

\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}

\mathbf{ x^2= \dfrac{2000000}{3} }

\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }

\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}

Now, if we replace the value with equation (1), then y will be:

\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\  \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}

\mathbf{x =500\sqrt{6}}

Now, the shortest length of the fencing can be computed by using the equation (2):

L = 3x + 2y

\mathbf{L = 3( \dfrac{1000  \sqrt{6}}{3}) + 2(500 \sqrt{6})}

\mathbf{L =1000  \sqrt{6} + 1000 \sqrt{6}}

\mathbf{L =2000  \sqrt{6} }

\mathbf{L \simeq 4899 \ ft}

Learn more about the area of a rectangle here:

brainly.com/question/25292087

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