zoe invested $370 in an account paying an interest rate of 4.2% compounded quarterly. assuming no deposits…

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=$370$, $r = 4.2%=0.042$, $n = 4$ (compounded quarterly), and $t = 12$ years.

Step3: Substitute values into the formula

$A=370(1 +\frac{0.042}{4})^{4\times12}$. First, calculate the value inside the parentheses: $\frac{0.042}{4}=0.0105$, then $1+\frac{0.042}{4}=1 + 0.0105=1.0105$. Next, calculate the exponent: $4\times12 = 48$. So, $A = 370\times(1.0105)^{48}$.

Step4: Calculate the final amount

$(1.0105)^{48}\approx1.61277$. Then $A=370\times1.61277\approx596.7249$. Rounding to the nearest cent, $A\approx$596.72$.

Answer:

$$596.72$