\begin{tabular}{l} Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra \( \$ 29,000 \) over the next 6 years. What amount \\ must be deposited quarterly into an account that earns \( 5.9 \% \) interest, compounded quarterly, in order to reach your goal? Round your answer to \\ the nearest cent, if necessary. \\ AnswerHow to enter your answer (opens in new window) 2 Points \\ Kormulas \\ Keyboard Shortcuts \\ Prev Keypad \\ \hline\end{tabular}

To find out how much you need to deposit quarterly to save $29,000 in 6 years at an interest rate of 5.9% compounded quarterly, you can use the future value of an annuity formula: \[ FV = P \times \frac{(1 + r/n)^{nt} - 1}{r/n} \] Where: - \( FV \) is the future value ($29,000) - \( P \) is the payment (the amount to be determined) - \( r \) is the annual interest rate (5.9% or 0.059) - \( n \) is the number of times the interest is compounded per year (4 for quarterly) - \( t \) is the number of years (6) Plugging in the numbers will help you solve for \( P \): \[ 29000 = P \times \frac{(1 + 0.059/4)^{4 \times 6} - 1}{0.059/4} \] Now, you'll be able to find that amount! To put this into real-world perspective, consider this: saving for a car in this manner teaches you disciplined financial habits. Each deposit is not only a step closer to that shiny new vehicle but also a way to better manage your finances for future purchases. Think of every quarter as a mini-celebration towards your goal! Lastly, common mistakes include forgetting to respect the compounding periods. Always ensure you're matching up deposits with the compounding frequency (quarterly, in this case) and keeping track of time properly. Otherwise, you may find yourself a few thousand short when it's time to buy that dream car!