benjamin invested $36,000 in an account paying an interest rate of 5.7% compounded quarterly. assuming no…

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=$36000$, the annual interest rate $r = 5.7%=0.057$, the number of times compounded per year $n = 4$ (compounded quarterly), and the time $t = 8$ years.

Step3: Substitute values into the formula

$A=36000(1 +\frac{0.057}{4})^{4\times8}$. First, calculate the value inside the parentheses: $\frac{0.057}{4}=0.01425$, and $1 + 0.01425=1.01425$. Then, calculate the exponent: $4\times8 = 32$. So, $A = 36000\times(1.01425)^{32}$.

Step4: Calculate $(1.01425)^{32}$

Using a calculator, $(1.01425)^{32}\approx1.56777$.

Step5: Calculate the final amount $A$

$A=36000\times1.56777 = 56439.72$. Rounding to the nearest dollar, $A\approx56440$.

Answer:

$56440$