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Otrada [13]
3 years ago
13

Gilbert is graduating from college in one year, but he will need a loan in the amount of $5,125 for his last two semesters. He m

ay either receive an unsubsidized Stafford Loan with an interest rate of 6.8%, compounded monthly, or his parents may get a PLUS Loan with an interest rate of 7.8%, compounded monthly. The Stafford Loan has a grace period of six months from the time of graduation. Which loan will have a higher balance at the time of repayment and by how much?
Mathematics
1 answer:
sleet_krkn [62]3 years ago
7 0
First, determine the effective interests given both interest rates.

(1)   ieff = (1 + 0.068/12)^12 - 1 = 0.07016
(2)   ieff = (1 + 0.078/12)^12 - 1 = 0.08085

Calculating the interests will entail us to use the equation,
     I = P ((1 + i)^n - 1)

Substituting the known values,
  (1)    I = ($5125)((1 + 0.07016)^1/2 - 1)
          I = $176.737

   (2)    I = ($5125)(1 + 0.08085)^1/2 - 1)
            I = $203.15

a. Hence, the greater interest will be that of the second loan. 

b. The difference between the interests,
    d = $203.15 - $176.737
          $26.413
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The length of the rectangle = 16 meters

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<u>Step-by-step explanation</u>:

Given that,

The Area of the rectangle is 273.

<u><em>Step 1</em></u><em> :</em>

Let, the width of the rectangle be 'x'

The length of the rectangle is 2x - 5

<u><em>Step 2</em></u><em> :</em>

Area of the rectangle = length \times width

                             273 = (2x - 5) x

                             273 = 2x^2 - 5x

<u><em>Step 3</em></u><em> :</em>

The equation formed is 2x^2 - 5x -273 = 0

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b= coefficient of x = -5

c = constant = -273

Find the roots of the equation, to find the width.

<u><em>Step 4</em></u><em> :</em>

Find the roots using factorizing method,

ac = 2\times-273 = -546 and b= -5

Factorizing -546 as -26\times21

The product of -26\times21 = -546

The sum of -26 + 21 = -5

<u><em>Step 5</em></u><em> :</em>

The roots of the equation 2x^2 - 5x -273 = 0 are x= -26/2 and x= 21/2

The values of x are x= -13 and x= 10.5

Since the width cannot be a negative value, neglect x= -13

<u><em>Step 6</em></u><em> :</em>

Therefore,

The width of the rectangle = 10.5 meters

The length of the rectangle = 2x-5

                                                = 2(10.5) - 5

                                                = 21 - 5

                                    length = 16 meters

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