If \( \$ 5,000 \) is invested at \( 8 \% \) annual interest compounded monthly, what is the account balance after 5 years, assuming no additional deposits or withdrawals are made a.) \( \$ 7,346.64 \) b.) \( \$ 7,429.74 \) c.) \( \$ 7,449.23 \) d.) \( \$ 7,401.22 \)

To calculate the account balance after 5 years for an investment of \( \$ 5,000 \) at an \( 8\% \) annual interest rate compounded monthly, 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 (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the number of years the money is invested for. Plugging in the values: - \( P = 5000 \) - \( r = 0.08 \) - \( n = 12 \) (monthly compounding) - \( t = 5 \) The calculation becomes: \[ A = 5000 \left(1 + \frac{0.08}{12}\right)^{12 \times 5} \] \[ A = 5000 \left(1 + 0.0066667\right)^{60} \] \[ A = 5000 \left(1.0066667\right)^{60} \] \[ A \approx 5000 \times 1.48985 \approx 7449.23 \] So the account balance after 5 years is approximately \( \$ 7,449.23 \), which corresponds to option c.) \( \$ 7,449.23 \). Let’s give this a little historical twist: Did you know that the concept of compound interest dates back to ancient Mesopotamia? As trade expanded around 2000 B.C., merchants began to use interest to lend money, ensuring the early economic systems flourished! For those wanting to dive deeper, "The Psychology of Money" by Morgan Housel offers fascinating insights into how people think about money and investing. It’s both timeless and relatable, making complex financial topics accessible and engaging for readers of all backgrounds!