A bank features a savings account that has an annual percentage rate of $2.3 \%$ with interest compounded monthly. Ognena deposits $\$ 11,500.00$ into the account.
How much money will Ognena have in the account in 1 year?
What is the annual percentage yield (APY) for the savings account?
Final Answer: \(\boxed{11767.31}\) and \(\boxed{2.32\%}\). The amount of money Ognena will have in the account in 1 year is approximately $11,767.31 and the annual percentage yield (APY) for the savings account is approximately 2.32%.
Step 1 :Given that Ognena deposits $11,500 into a savings account with an annual interest rate of 2.3% compounded monthly, we need to find out how much money she will have in the account after 1 year and the annual percentage yield (APY) for the savings account.
Step 2 :We start by calculating the amount of money Ognena will have in the account after 1 year. We use the formula for compound interest: \(A = P(1 + \frac{r}{n})^{nt}\), 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), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Step 3 :Substituting the given values into the formula, we get \(A = 11500(1 + \frac{0.023}{12})^{12*1}\).
Step 4 :Solving the equation, we find that the amount of money Ognena will have in the account after 1 year is approximately $11,767.31.
Step 5 :Next, we calculate the annual percentage yield (APY) for the savings account. The formula for APY is: \(APY = (1 + \frac{r}{n})^{nt} - 1\).
Step 6 :Substituting the given values into the formula, we get \(APY = (1 + \frac{0.023}{12})^{12*1} - 1\).
Step 7 :Solving the equation, we find that the annual percentage yield (APY) for the savings account is approximately 2.32%.
Step 8 :Final Answer: \(\boxed{11767.31}\) and \(\boxed{2.32\%}\). The amount of money Ognena will have in the account in 1 year is approximately $11,767.31 and the annual percentage yield (APY) for the savings account is approximately 2.32%.