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Porsha calculates the amount of money she will have at the end of 6 years on a $5,000 investment earning 3.75% interest compounded quarterly. She writes the following expression:5,000 (1 + 0.0375) superscript 24Which of the following statements about Porsha's expression is true?a.Porsha's expression is correct.b.Porsha's expression should have 1 + 0.009375 in the parentheses.c.Porsha's expression should have an exponent of 6, not 24.d.Porsha's expression should have both 1 + 0.009375 in the parentheses and an exponent of 6.

Respuesta :

Using the compound interest formula, it is found that the correct option is:

b. Porsha's expression should have 1 + 0.009375 in the parentheses.

Compound interest:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

  • A(t) is the amount of money after t years.  
  • P is the principal(the initial sum of money).  
  • r is the interest rate(as a decimal value).  
  • n is the number of times that interest is compounded per year.  
  • t is the time in years for which the money is invested or borrowed.

In this problem:

  • Investment of $5,000, thus [tex]P = 5000[/tex].
  • Interest rate of 3.75%, thus [tex]r = 0.0375[/tex].
  • 6 years, thus [tex]t = 6[/tex]
  • Compounded quarterly, thus [tex]n = 4[/tex].

Then, the amount is:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(t) = 5000(1 + \frac{0.0375}{4})^{4(6)}[/tex]

[tex]A(t) = 5000(1 + 0.009375)^{24}[/tex]

Thus, her error is in the parentheses, and the correct option is:

b. Porsha's expression should have 1 + 0.009375 in the parentheses.

A similar problem is given at https://brainly.com/question/25195489

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