use the given information to find the balance in the account earning compound interest after 6 years when…

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 $P = 3500$, the annual interest rate $r=2.16%=0.0216$, the number of times compounded per year $n = 4$ (since it's compounded quarterly), and the time $t = 6$ years.

Step3: Substitute values into the formula

$A=3500(1 +\frac{0.0216}{4})^{4\times6}$. First, calculate the value inside the parentheses: $\frac{0.0216}{4}=0.0054$, then $1+\frac{0.0216}{4}=1 + 0.0054=1.0054$. Next, calculate the exponent: $4\times6 = 24$. So, $A = 3500\times(1.0054)^{24}$.

Step4: Calculate $(1.0054)^{24}$

Using a calculator, $(1.0054)^{24}\approx1.13477$.

Step5: Calculate the final amount

$A=3500\times1.13477 = 3971.695\approx3971.70$.

Answer:

$3971.70$