Let's break down the given equation: [tex]\(A=2,400\left(1+\frac{0.031}{4}\right)^{21}\)[/tex].
This equation appears to be in the standard form of the compound interest formula:
[tex]\[A = P \left(1 + \frac{r}{n}\right)^{nt},\][/tex]
where:
- [tex]\(A\)[/tex] is the amount of money accumulated after [tex]\(n\)[/tex] periods,
- [tex]\(P\)[/tex] is the principal amount (initial investment),
- [tex]\(r\)[/tex] is the annual interest rate,
- [tex]\(n\)[/tex] is the number of times interest is compounded per year,
- [tex]\(t\)[/tex] is the time the money is invested for in years.
From the equation:
- [tex]\(P\)[/tex] is 2400, representing the initial investment.
- The expression [tex]\(\left(1 + \frac{0.031}{4}\right)\)[/tex] implies that the annual interest rate is [tex]\(0.031\)[/tex], and it is compounded quarterly (4 times a year).
- The exponent [tex]\(21\)[/tex] represents the total number of compounding periods.
Now, focusing on the value [tex]\(0.031\)[/tex]:
The fraction [tex]\(\frac{0.031}{4}\)[/tex] indicates that [tex]\(0.031\)[/tex] is divided by 4, which fits the structure of the compound interest formula. In this context, [tex]\(0.031\)[/tex] is the annual interest rate before being divided by the number of compounding periods per year. Therefore, the value [tex]\(0.031\)[/tex] represents the annual interest rate.
Given this analysis, the annual interest rate [tex]\(0.031\)[/tex] translates to [tex]\(3.1\%\)[/tex].
Thus, the correct interpretation is:
The value 0.031 represents the interest rate, which means the annual compounded interest rate is [tex]\(3.1\%\)[/tex].
