7. [0/0.6 Points] DETAILS \( _{\text {MY NOTES }} \) AUFEXC4 11.2.027. 1/100 Submissions Used Calculate the future value of \( \$ 6,000 \) earning \( 7 \% \) interest compounded quarterly for 6 years. (Round your answer to
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The Deep Dive
To find the future value of an investment compounded quarterly, you can use the formula: \[ FV = P \times \left(1 + \frac{r}{n}\right)^{nt} \] where \( P \) is the principal amount (initial investment), \( r \) is the annual interest rate (decimal), \( n \) is the number of times interest is compounded per year, and \( t \) is the number of years. For your example, with \( P = 6000 \), \( r = 0.07 \), \( n = 4 \), and \( t = 6 \), the calculation gives you a future value of approximately \( \$ 9,098.24 \). Now, let’s talk about how this applies in real life! People often use compounding to grow their savings, like for retirement funds. By investing now and allowing interest to compound over time, you can substantially increase your savings while you focus on other things in life. It's money making money! Lastly, one common mistake is forgetting to convert the interest rate into decimal form or not properly handling the compounding frequency. Always double-check your values! Remember, using a financial calculator or spreadsheet software can also simplify this process and reduce errors.
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