Angela deposits \( \$ 2500 \) into an account with an APR of \( 2.7 \% \) for 7 years. Find the future value of the account if interest is compounded monthly. Round your answer to the nearest hundredth, 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 \[ \begin{array}{l} A=P e^{r t} \\ A P Y=\left(1+\frac{r}{n}\right)^{n}-1 \end{array} \] Answer

To find the future value of Angela's account with compound interest, we'll use the formula \( A = P\left(1+\frac{r}{n}\right)^{nt} \). Here, \( P = 2500 \), \( r = 0.027 \), \( n = 12 \) (for monthly compounding), and \( t = 7 \). First, we calculate \( A \): \[ A = 2500\left(1+\frac{0.027}{12}\right)^{12 \times 7} \] Next, we find \( \frac{0.027}{12} \approx 0.00225 \) and compute: \[ A = 2500\left(1+0.00225\right)^{84} \] \[ A = 2500\left(1.00225\right)^{84} \] Using a calculator, \( (1.00225)^{84} \approx 1.21167 \). So, \[ A \approx 2500 \times 1.21167 \approx 3029.18 \] Therefore, the future value of Angela's account after 7 years is approximately \( \boxed{3029.18} \). Now for some fun facts: When interest is compounded, it can really work wonders for your savings! Over time, compounding can lead to exponential growth rather than just linear. This means your interest earns interest, so it’s like a little money-making machine! For those looking to dive deeper, the concept of compounding is not just limited to savings accounts. It's the same principle behind investment growth in stocks, dividends, and even retirement savings plans like 401(k)s. There are plenty of resources like books and online courses that delve deeper into financial growth strategies and smart investing!