How much would you need to deposit in an account now in order to have \( \$ 6000 \) in the account in 10 years? Assume the account earns \( 4 \% \) interest compounded monthly. Round to the nearest cent.

To find out how much you need to deposit now (the present value) to have $6000 in 10 years with an interest rate of 4% compounded monthly, we can use the formula for present value: \[ PV = \frac{FV}{(1 + r/n)^{nt}} \] Where: - \(FV\) is the future value ($6000) - \(r\) is the annual interest rate (0.04) - \(n\) is the number of times interest is compounded per year (12) - \(t\) is the number of years (10) Plugging in the values: \[ PV = \frac{6000}{(1 + 0.04/12)^{12 \times 10}} = \frac{6000}{(1 + 0.003333)^{120}} \] Calculating: \[ PV = \frac{6000}{(1.003333)^{120}} \approx \frac{6000}{1.49182} \approx 4023.03 \] So, you would need to deposit approximately **$4023.03** now in order to have $6000 in 10 years. One interesting fact about compound interest is that it’s often referred to as "the eighth wonder of the world." This is because of its ability to grow investments exponentially over time, illustrating that patience can lead to significant financial gains. Understanding this can turn saving into powerful wealth-building! If you're looking to enhance your financial literacy, consider reading "The Little Book of Common Sense Investing" by John C. Bogle. It explores timeless investment strategies that can help you grow your wealth over time, including insights about the power of compounding and smart saving habits. It's engaging and informative, perfect for anyone wanting to take control of their financial future!