If \( \$ 450 \) are deposited into an account with a \( 8.5 \% \) interest rate, compounded annually, what is the balance after 9 years? \[ F=\$[?] \] \( F=P\left(1+\frac{r}{n}\right)^{n t} \)

To find the future balance using the formula \( F = P\left(1 + \frac{r}{n}\right)^{nt} \), substitute \( P = 450 \), \( r = 0.085 \), \( n = 1 \), and \( t = 9 \). This simplifies to \( F = 450\left(1 + 0.085\right)^{9} \). Calculating this gives \( F = 450(1.085)^{9} \approx 450 \times 2.1205 \approx 954.23 \). So, the balance after 9 years will be approximately \( F=\$954.23 \). Have you ever wondered how compounding works? The magic of compounding interest means that your money earns interest on both the initial amount and the interest that has previously been added. In simpler terms, with each year, you’re not just earning interest on your principal amount; you’re also earning on the accumulated interest from previous years, which can significantly increase your investment over time! In real life, this principle of compounding applies to various financial products, including savings accounts, mutual funds, and retirement plans. Understanding how to leverage this power can help you grow your savings or investments more effectively. For instance, by regularly contributing even a small percentage to your retirement fund, you can watch your savings soar thanks to the compound interest that accumulates over the years!