you deposit $500 in an account that pays 2.5% annual interest. find the balance after 2 years when the…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula when compounded $n$ times a year 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. Here, $P = 500$, $r=0.025$ (since $2.5%=0.025$), $n = 365$ (compounded daily), and $t = 2$.

Step2: Substitute values into the formula

$A=500(1 +\frac{0.025}{365})^{365\times2}$. First, calculate $\frac{0.025}{365}\approx0.0000684932$. Then $1+\frac{0.025}{365}=1 + 0.0000684932=1.0000684932$. Next, $365\times2 = 730$. So $A = 500\times(1.0000684932)^{730}$. Using a calculator, $(1.0000684932)^{730}\approx1.05127$. Then $A=500\times1.05127 = 525.635\approx525.64$.

Answer:

$525.64$