Question 1 of 14. Step 1 of 1 \( 0 / 14 \) Correct David deposits \( \$ 3000 \). Determine the APY if there is an APR of \( 4.5 \% \) compounded monthly. Express your answer as a percentage rounded to the nearest hundredth of a percent, if necessary. Formulas Simple Interest \[ \begin{array}{l} I=P r t \\ A=P(1+r t) \\ A=P\left(1+\frac{r}{n}\right)^{n t} \end{array} \] Future Value for Simple Interest Future Value for Compound Interest Future Value for Continuous Compound Interest \[ \begin{array}{l} A=P e^{n t} \\ A P Y=\left(1+\frac{r}{n}\right)^{n}-1 \end{array} \] Annual Percentage Yield (APY) Answer

To find the APY given an APR of \( 4.5\% \) compounded monthly, we can use the formula for APY: \[ APY = \left(1 + \frac{r}{n}\right)^{n} - 1 \] In this case, \( r = 0.045 \) (4.5% expressed as a decimal) and \( n = 12 \) (number of compounding periods per year). Plugging these values in: \[ APY = \left(1 + \frac{0.045}{12}\right)^{12} - 1 \] Calculating it gives: \[ APY = \left(1 + 0.00375\right)^{12} - 1 \approx 0.0458607 \] Converting to percentage: \[ APY \approx 4.59\% \] So, the APY is approximately **4.59%** when rounded to the nearest hundredth of a percent. Got it? Let’s dive into some additional context! The concept of compounding interest dates back centuries and has played a pivotal role in finance ever since ancient civilizations started lending and borrowing. By compounding, you earn interest not just on the principal, but also on the interest that accumulates over time, which can significantly increase your total return. It’s like watching your money grow exponentially, thanks to the magic of mathematics! If you want to maximize your savings, keeping an eye on APY is essential. It directly reflects how much you’ll earn on your deposits compared to APR, which only measures the interest without considering compounding effects. Saving in accounts with higher APYs can lead to much greater financial benefits in the long run. So don’t just look at the rates—dig deeper into the compounding frequency!