mai deposited $4000 into an account with 5% interest, compounded quarterly. assuming that no withdrawals are…

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 $P = 4000$, the annual interest rate $r=0.05$ (since $5%= 0.05$), the number of times compounded per year $n = 4$ (compounded quarterly), and the time $t = 7$ years.

Step3: Substitute values into the formula

$A=4000(1 +\frac{0.05}{4})^{4\times7}$. First, calculate the value inside the parentheses: $\frac{0.05}{4}=0.0125$, then $1+\frac{0.05}{4}=1 + 0.0125=1.0125$. Next, calculate the exponent: $4\times7 = 28$. So, $A = 4000\times(1.0125)^{28}$.

Step4: Calculate the final amount

$(1.0125)^{28}\approx1.412973$. Then $A=4000\times1.412973 = 5651.892$. Rounding to the nearest cent, $A\approx$5651.89$.

Answer:

$5651.89$