bao invested $510 in an account paying an interest rate of 3.7% compounded monthly. assuming no deposits or…

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 $P = 510$, the annual interest rate $r=0.037$ (since $3.7%=0.037$), the number of times compounded per year $n = 12$ (compounded monthly), and the time $t = 5$ years.

Step3: Substitute values into the formula

$A=510(1 +\frac{0.037}{12})^{12\times5}$. First, calculate the value inside the parentheses: $\frac{0.037}{12}\approx0.0030833$, then $1+\frac{0.037}{12}=1 + 0.0030833=1.0030833$. Next, calculate the exponent: $12\times5 = 60$. So, $A = 510\times(1.0030833)^{60}$.

Step4: Calculate the final amount

$(1.0030833)^{60}\approx1.20277$. Then $A=510\times1.20277\approx613.4127$. Rounding to the nearest dollar, $A\approx613$.

Answer:

$613$