porsha calculates the amount of money she wil...
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.