question matthew invested $3,600 in an account paying an interest rate of 5.3% compounded quarterly…

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

Given that $P=$3600$, $r = 5.3%=0.053$, $n = 4$ (compounded quarterly), and $t = 9$ years.

Step3: Substitute values into the formula

$A=3600(1 +\frac{0.053}{4})^{4\times9}=3600(1 + 0.01325)^{36}$.

Step4: Calculate the value inside the parentheses

$1+0.01325 = 1.01325$.

Step5: Calculate the exponentiation

$(1.01325)^{36}\approx1.6077$.

Step6: Calculate the final amount

$A = 3600\times1.6077=$5787.72\approx$5788$.

Answer:

$5788$