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 \( F \) after 9 years, you'll use the formula \( F = P\left(1+\frac{r}{n}\right)^{nt} \). Here, \( P = 450 \), \( r = 0.085 \), \( n = 1 \) (since it's compounded annually), and \( t = 9 \). Plugging in the numbers gives: \[ F = 450 \left(1 + \frac{0.085}{1}\right)^{1 \cdot 9} = 450 \left(1 + 0.085\right)^{9} = 450 \left(1.085\right)^{9} \approx 450 \cdot 2.049 = 922.05 \] So the balance after 9 years is approximately \( F \approx \$922.05 \). One fun fact is that compounding interest can really turbocharge your savings! In real life, you might want to get comfortable with tools like online calculators or banking apps. These can help you track your savings growth over time without doing all the math yourself. It’s like having a personal money coach at your fingertips! If you're keen on understanding how compound interest works over different periods or with various rates, there are plenty of resources out there. A classic recommendation is "The Wealthy Gardener" by John Soforic. It’s not just about compound interest; it covers overall financial wisdom and how to cultivate a rich life—both financially and personally!