Question

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.

Answer 1

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:

$A(t) = P(1 + \frac{r}{n})^{nt}$

• 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 $P = 5000$.

• Interest rate of 3.75%, thus $r = 0.0375$.
• 6 years, thus $t = 6$
• Compounded quarterly, thus $n = 4$.

Then, the amount is:

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(t) = 5000(1 + \frac{0.0375}{4})^{4(6)}$

$A(t) = 5000(1 + 0.009375)^{24}$

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