find the amount that results from the given investment. $500 invested at 12% compounded daily after a period…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula when compounded $n$ times a year 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 have $P = 500$, $r=0.12$ (since $12%=0.12$), $n = 365$ (compounded daily), and $t = 2$.

Step3: Substitute the values into the formula

$A=500(1 +\frac{0.12}{365})^{365\times2}$. First, calculate the value inside the parentheses: $\frac{0.12}{365}\approx0.000328767$, then $1+\frac{0.12}{365}=1 + 0.000328767=1.000328767$. Next, calculate the exponent: $365\times2 = 730$. So, $A = 500\times(1.000328767)^{730}$. Using a calculator, $(1.000328767)^{730}\approx1.271221$. Then $A = 500\times1.271221=635.6105$.

Step4: Round to the nearest cent

Rounding $635.6105$ to the nearest cent gives $A\approx635.61$.

Answer:

$635.61$