question 5\nscore on last try: 0 of 4 pts. see details for more.\nat least one scored part is incorrect…
question 5\nscore on last try: 0 of 4 pts. see details for more.\nat least one scored part is incorrect. jump to first changable incorrect part.\nget a similar question you can retry this question below\na bank features a savings account that has an annual percentage rate of 5.8 % with interest compounded monthly. nahele deposits $5,500 into the account.\nhow much money will nahele have in the account in 1 year?\nanswer = $ \nround answer to the nearest penny.\nwhat is the annual percentage yield (apy) for the savings account?\napy = \nround to the nearest hundredth of a percent.
Answer
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. Here, $P = 5500$, $r=0.058$, $n = 12$ (compounded monthly), and $t = 1$. $A=5500(1 +\frac{0.058}{12})^{12\times1}$
Step2: Calculate the amount after 1 year
First, calculate the value inside the parentheses: $\frac{0.058}{12}\approx0.004833$. Then $1+\frac{0.058}{12}=1 + 0.004833=1.004833$. $(1.004833)^{12}\approx1.05957$. $A = 5500\times1.05957=5827.635\approx5827.64$.
Step3: Calculate the APY formula
The APY formula is $APY=(1+\frac{r}{n})^{n}-1$. Substitute $r = 0.058$ and $n = 12$ into the formula: $(1+\frac{0.058}{12})^{12}-1$. We already know that $(1+\frac{0.058}{12})^{12}\approx1.05957$. $APY=1.05957 - 1=0.05957$. Convert to percentage: $APY = 5.96%$ (rounded to the nearest hundredth of a percent).
Answer:
$5827.64$ $5.96$