arianna invested $530 in an account paying an interest rate of 5.7% compounded monthly. assuming no deposits…

Explanation:

Step1: Identify the 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 the given values to the appropriate form

We are given that $P=$530$, $r = 5.7%=0.057$, $n = 12$ (compounded monthly), and $t = 5$ years.

Step3: Substitute the values into the formula

$A=530(1 +\frac{0.057}{12})^{12\times5}$. First, calculate the value inside the parentheses: $\frac{0.057}{12}=0.00475$, then $1+\frac{0.057}{12}=1 + 0.00475=1.00475$. Next, calculate the exponent: $12\times5 = 60$. So, $A = 530\times(1.00475)^{60}$.

Step4: Calculate $(1.00475)^{60}$

Using a calculator, $(1.00475)^{60}\approx1.32107$.

Step5: Calculate the value of $A$

$A=530\times1.32107\approx709.1671$. Rounding to the nearest dollar, $A\approx709$.

Answer:

$709$