A bank features a savings account that has an annual percentage rate of \( 3 \% \) with interest compounded monthly. Marissa deposits \( \$ 9,000 \) into the account. How much money will Marissa have in the account in 1 year? Answer \( =\$ \square \) Round answer to the nearest penny. What is the annual percentage yield (APY) for the savings account? APY \( =\square \% \) Round to the nearest hundredth of a percent. Question Help: Message instructor Qilculator

To find out how much money Marissa will have in her account after a year with interest compounded monthly, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial money Marissa deposited, which is \( \$9,000 \)). - \( r \) is the annual interest rate (decimal) (which is \( 0.03 \)). - \( n \) is the number of times that interest is compounded per year (which is \( 12 \) for monthly). - \( t \) is the number of years the money is invested or borrowed (which is \( 1 \) year). Plugging in the numbers: \[ A = 9000 \left(1 + \frac{0.03}{12}\right)^{12 \times 1} \] Calculating this will give us: \[ A \approx 9000 \left(1 + 0.0025\right)^{12} \approx 9000 \left(1.0304\right) \approx 9273.60 \] So, Marissa will have approximately \( \$9,273.60 \) in the account after one year. To find the annual percentage yield (APY), we can use the formula: \[ APY = \left(1 + \frac{r}{n}\right)^{n} - 1 \] Substituting the values: \[ APY = \left(1 + \frac{0.03}{12}\right)^{12} - 1 = \left(1.0025\right)^{12} - 1 \approx 0.0304 \] To express this as a percentage: \[ APY \approx 0.0304 \times 100 \approx 3.04\% \] Therefore, the answers are: Answer \( = \$9,273.60 \) APY \( = 3.04\% \) Did you know that the concept of compound interest dates back to ancient civilizations? One of the earliest records of its use can be traced to the Babylonians, who had strategies for calculating interest on loans over three thousand years ago! For those looking to dive deeper into the world of savings and investment, consider reading “The Intelligent Investor” by Benjamin Graham. It’s a classic book that delves into investment strategies and principles while also covering the importance of understanding compound interest—after all, the best time to start saving was yesterday!