select the correct answer. the function f(x)=2500(1 + 0.021/365)^365t models the balance in a savings…

select the correct answer. the function f(x)=2500(1 + 0.021/365)^365t models the balance in a savings account. which statement accurately describes the account? a. the account had an initial balance of $2500 and compounds monthly at an annual interest rate of 2.1%. b. the account had an initial balance of $2500 and compounds yearly at an annual interest rate of 2.1%. c. the account had an initial balance of $2500 and compounds daily at an annual interest rate of 0.21%. d. the account had an initial balance of $2500 and compounds daily at an annual interest rate of 2.1%.

select the correct answer. the function f(x)=2500(1 + 0.021/365)^365t models the balance in a savings account. which statement accurately describes the account? a. the account had an initial balance of $2500 and compounds monthly at an annual interest rate of 2.1%. b. the account had an initial balance of $2500 and compounds yearly at an annual interest rate of 2.1%. c. the account had an initial balance of $2500 and compounds daily at an annual interest rate of 0.21%. d. the account had an initial balance of $2500 and compounds daily at an annual interest rate of 2.1%.

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula for compounding $n$ times a year is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount (initial balance), $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years. In the given function $f(x)=2500(1 +\frac{0.021}{365})^{365t}$, $P = 2500$, $r=0.021$ (2.1% annual interest rate), and $n = 365$ (compounded daily).

Answer:

D. The account had an initial balance of $2,500 and compounds daily at an annual interest rate of 2.1%.