debra deposited $4000 into an account with 4.2% interest, compounded quarterly. assuming that no withdrawals…

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 $P = 4000$, $r=0.042$ (since $4.2%=0.042$), $n = 4$ (compounded quarterly), and $t = 9$.

Step3: Substitute values into the formula

$A=4000(1 +\frac{0.042}{4})^{4\times9}=4000(1 + 0.0105)^{36}$.

Step4: Calculate the value inside the parentheses

$1+0.0105 = 1.0105$.

Step5: Calculate the exponentiation

$(1.0105)^{36}\approx1.446577$.

Step6: Calculate the final amount

$A = 4000\times1.446577=5786.308$.

Answer:

$$5786.31$