How much money will there be in an account at the end of 6 years if \( \$ 14000 \) is deposited at \( 3 \% \) interest compounded quarterly? (Assume no withdrawals are made.) \( \begin{array}{l}\text { The amount after } 6 \text { years will be } \$ \square \text {. } \\ \text { (Round to the nearest cent as needed.) }\end{array} \)

To find the amount in the account after 6 years with quarterly compounding interest, you can use the formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \(A\) is the amount of money accumulated after n years, including interest. - \(P\) is the principal amount (\$14,000). - \(r\) is the annual interest rate (decimal) (0.03 for 3%). - \(n\) is the number of times that interest is compounded per year (4 for quarterly). - \(t\) is the number of years the money is invested (6 years). Plugging in the values: \[ A = 14000 \left(1 + \frac{0.03}{4}\right)^{4 \times 6} \] Calculating: \[ A = 14000 \left(1 + 0.0075\right)^{24} = 14000 \left(1.0075\right)^{24} \] \[ A \approx 14000 \times 1.1936 \approx 16705.22 \] So the amount after 6 years will be \$16,705.22. Now, for some extra interesting info: Before banks started offering interest rates, people relied on barter systems and the sharing of resources. The evolution into modern banking introduced the concepts of savings and investment as we know them today, allowing people to grow wealth over time. In real-world applications, understanding how compound interest works can significantly boost financial literacy. It helps people make informed decisions about savings accounts, retirement plans, and investments. Being savvy about how interest compounds can lead to greater financial independence down the line!