jeriel invested $4,200 in an account paying an interest rate of 5.5% compounded monthly. assuming no…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Given $P = 4200$, $r=0.055$ (since $5.5%=0.055$), $n = 12$ (compounded monthly), and $t = 7$.

Step2: Substitute the values into the formula

Substitute the values into the formula: [ \begin{align*} A&=4200\left(1 +\frac{0.055}{12}\right)^{12\times7}\ &=4200\left(1+\frac{0.055}{12}\right)^{84} \end{align*} ] First, calculate $\frac{0.055}{12}\approx0.004583$. Then $1+\frac{0.055}{12}\approx1.004583$. Next, calculate $(1.004583)^{84}$. Using a calculator, $(1.004583)^{84}\approx1.4579$. Then $A = 4200\times1.4579$.

Step3: Calculate the final amount

$A=4200\times1.4579 = 6123.18$.

Answer:

$6120$ (rounded to the nearest ten dollars)