Question 6 of 14, 5 tep 1 of 1 A couple deposits \( \$ 21,000 \) into an account earning \( 6 \% \) annual interest for 15 years. Calculate the future value of the investment if the interest is compounded weekly, Round your answer to the nearest cent. Answer How to enter your answer (opens in new window) Formulas Keyboard Shortcuts

The future value (FV) of an investment can be calculated using the formula: \[ FV = P \left(1 + \frac{r}{n}\right)^{nt} \] where \( P \) is the principal amount (initial deposit), \( r \) is the annual interest rate (decimal), \( n \) is the number of times the interest is compounded per year, and \( t \) is the number of years. For your scenario, \( P = 21,000 \), \( r = 0.06 \), \( n = 52 \), and \( t = 15 \). Plugging in these values: \[ FV = 21000 \left(1 + \frac{0.06}{52}\right)^{52 \times 15} \]. Using a calculator, you'll find the future value is approximately \( \$ 85,475.89 \). Ever wondered how your investment choices would change over time? Well, compounding interest is like planting a seed and watching it grow exponentially. The more frequently the interest is compounded, the more you reap from that financial harvest! Weekly compounding means your money isn't just sitting there; it's busy working for you even when you're not looking. As exciting as it is to see those numbers grow, remember to check your calculations. Common mistakes include forgetting to convert the interest rate from a percentage to a decimal and overlooking the compounding frequency. A tiny misstep can lead to significant differences, especially over 15 years! Always double-check your inputs before hitting that calculate button.