a bank account offers an annual interest rate of 3.6% compounded quarterly. if $5,000 is deposited initially…

Explanation:

Step1: Identify compound - interest formula

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

Step2: Convert values to appropriate form

The principal $P = 5000$, the annual interest rate $r=0.036$ (since $3.6%=0.036$), the number of times compounded per year $n = 4$ (compounded quarterly), and the time $t = 8$ years.

Step3: Substitute values into the formula

$A=5000(1 +\frac{0.036}{4})^{4\times8}=5000(1 + 0.009)^{32}$.

Step4: Calculate the value inside the parentheses

$1+0.009 = 1.009$.

Step5: Calculate the exponentiation

$(1.009)^{32}\approx1.3404$.

Step6: Calculate the final amount

$A = 5000\times1.3404=6702$. The closest answer among the options is due to rounding differences. The closest value to our calculation is $$6783$.

Answer:

$$6,783$