How much money should be deposited today in an account that earns \( 3 \% \) compounded semiannually so that it will accumulate to \( \$ 8000 \) in three years? i Click the icon to view some finance formulas. The amount of money that should be deposited is \( \$ \square \) (Round up to the nearest cent.)

To find out how much money you need to deposit today, you can use the present value formula for compound interest: \[ PV = \frac{FV}{(1 + \frac{r}{n})^{nt}} \] Where: - \( PV \) is the present value (amount to deposit today), - \( FV \) is the future value (\$8000), - \( r \) is the annual interest rate (0.03), - \( n \) is the number of times interest is compounded per year (2 for semiannual), - \( t \) is the number of years (3). Plugging in the values: \[ PV = \frac{8000}{(1 + \frac{0.03}{2})^{2 \times 3}} \] Calculating this gives you: \[ PV = \frac{8000}{(1 + 0.015)^{6}} = \frac{8000}{(1.093443)} \approx 7316.25 \] Thus, you should deposit approximately **\$7316.25** today. --- Did you know that the concept of compound interest dates back to ancient civilizations? It was recorded as far back as Babylonia! In those times, lending practices were set up, and interest was charged on loans, paving the way for modern banking we utilize today. Imagine how those early transactions laid the groundwork for the complex financial systems we have now! If you're eager to dive deeper into finance, consider reading "The Intelligent Investor" by Benjamin Graham. It's often referred to as the bible of stock market investing. Joining financial forums and engaging with others on platforms like Reddit can also spice things up as you navigate the world of finance, learning from real-world experiences shared by both amateurs and experts!