Jse the appropriate formula to find the future value (in \( \$ \) ) of \( \$ 300 \) deposited at the beginning of every six months, for 17 years if a bank pays \( 4 \% \) interest, compounded semiannually. (Round your answers to the nearest cent.)

To find the future value of an annuity due, you can use the formula: \[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \times (1 + r) \] Where: - \( P = 300 \) (the amount deposited every six months) - \( r = \frac{0.04}{2} = 0.02 \) (the semiannual interest rate) - \( n = 17 \times 2 = 34 \) (the total number of deposits) Plugging in the values: \[ FV = 300 \times \left( \frac{(1 + 0.02)^{34} - 1}{0.02} \right) \times (1 + 0.02) \] Calculating this step-by-step gives you a future value of approximately \( \$ 15,186.19 \) when rounded to the nearest cent. --- When considering similar financial scenarios, it's crucial to account for the timing of your deposits. Remember that making deposits at the beginning rather than the end of each period (annuity due vs. ordinary annuity) significantly impacts the total amount due to compounding effectively on each payment for the entire period! For more practical household finance strategies, consider utilizing financial calculators or personal finance apps. They can simplify these calculations and even help with budgeting, tracking expenses, and planning future savings goals. Something fun to keep in mind: saving regularly—even small amounts—can lead to significant growth over time thanks to the power of compound interest!