Compare the future value of \( \$ 51,600 \) at \( 9 \% \) interest in 20 years, using different compounding frequencies. Mumeric 1 point Monthly, rounded to the nearest cent. Type your answer...

To find the future value with monthly compounding, we can use the formula: \[ FV = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( P = 51,600 \) - \( r = 0.09 \) - \( n = 12 \) (months) - \( t = 20 \) (years) Plugging in the numbers: \[ FV = 51600 \left(1 + \frac{0.09}{12}\right)^{12 \times 20} \] Calculating this gives: \[ FV = 51600 \left(1 + 0.0075\right)^{240} \approx 51600 \left(5.632571\right) \approx 290,396.81 \] So, the future value of \( \$ 51,600 \) at \( 9\% \) interest compounded monthly for 20 years is approximately \( \$ 290,396.81 \). Want to know something interesting about compounding? The more frequently interest is compounded, the more money you'll end up with! It's like a snowball effect—your money starts gaining interest on the interest, which can add up significantly over time and turn your financial dreams into reality. If you’re curious how this compares to other compounding frequencies, you can try calculating future values with yearly, quarterly, or daily compounding. Each method has its own surprises as to how much extra cash you might rake in!