a deposit of $3,500 has an interest rate of 5% and is compounded quarterly. how much will be in the account…

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 given values to appropriate form

The principal $P=$3500$, the annual interest rate $r = 5%=0.05$, the number of times compounded per year $n = 4$ (compounded quarterly), and the time $t = 2.3$ years.

Step3: Substitute values into the formula

$A=3500(1 +\frac{0.05}{4})^{4\times2.3}$. First, calculate the value inside the parentheses: $\frac{0.05}{4}=0.0125$, then $1+\frac{0.05}{4}=1.0125$. Next, calculate the exponent: $4\times2.3 = 9.2$. So, $A = 3500\times(1.0125)^{9.2}$. $(1.0125)^{9.2}\approx1.1197$. Then $A=3500\times1.1197=$3918.95$.

Answer:

$$3918.95$