porsha calculates the amount of money she will have at the end of 6 years on a $5,000 investment earning…

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)^24. which of the following statements about porshas expression is true? a. porshas expression is correct. b. porshas expression should have 1 + 0.009375 in the parentheses. c. porshas expression should have an exponent of 6, not 24. d. porshas expression should have both 1 + 0.009375 in the parentheses and an exponent of 6. please select the best answer from the choices provided

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)^24. which of the following statements about porshas expression is true? a. porshas expression is correct. b. porshas expression should have 1 + 0.009375 in the parentheses. c. porshas expression should have an exponent of 6, not 24. d. porshas expression should have both 1 + 0.009375 in the parentheses and an exponent of 6. please select the best answer from the choices provided

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Identify given values

Here, $P = 5000$, $r=0.0375$, $n = 4$ (compounded quarterly), and $t = 6$.

Step3: Calculate the value inside the parentheses

$\frac{r}{n}=\frac{0.0375}{4}=0.009375$, so the value inside the parentheses should be $1 + 0.009375$.

Step4: Calculate the exponent

$nt=4\times6 = 24$.

Answer:

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