a bank features a savings account that has an annual percentage rate of 2.8% with interest compounded…

Explanation:

Step1: Identify 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=$9500$, $r = 0.028$ (since $2.8%=0.028$), $n = 12$ (compounded monthly), and $t = 1$. $A=9500(1 +\frac{0.028}{12})^{12\times1}$

Step2: Calculate the amount in the account after 1 year

First, calculate the value inside the parentheses: $\frac{0.028}{12}\approx0.002333$. Then $1+\frac{0.028}{12}=1 + 0.002333=1.002333$. $(1.002333)^{12}\approx1.02835$. $A = 9500\times1.02835=$9779.325\approx$9779.33$

Step3: Identify the APY formula

The APY formula is $APY=(1+\frac{r}{n})^{n}-1$. Substitute $r = 0.028$ and $n = 12$ into the formula: $APY=(1+\frac{0.028}{12})^{12}-1$

Step4: Calculate the APY

We already know that $(1+\frac{0.028}{12})^{12}\approx1.02835$. $APY=1.02835 - 1=0.02835$ or $2.835%$

Answer:

a) $$9779.33$ b) $2.835%$