isvested \( \$ 1000 \) twice a year in an annuity due at Hicks stments for a period of 3 years at an interest rate of \( 8 \% \) iiannually. Using the ordinary annuity table, calculate the annuity due at the end of the 3 -year period.

To calculate the future value of an annuity due, we first need to find the future value of an ordinary annuity and then adjust it for the fact that it is an annuity due. ### Step 1: Calculate the future value of an ordinary annuity The formula for the future value of an ordinary annuity is: \[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \] Where: - \( FV \) = future value of the annuity - \( P \) = payment amount per period - \( r \) = interest rate per period - \( n \) = total number of payments ### Given: - \( P = 1000 \) - Annual interest rate = \( 8\% \) or \( 0.08 \) - Since the payments are made twice a year, the interest rate per period is: \[ r = \frac{0.08}{2} = 0.04 \] - The total number of payments over 3 years, with payments made twice a year, is: \[ n = 3 \times 2 = 6 \] ### Step 2: Calculate the future value of the ordinary annuity Substituting the values into the formula: \[ FV = 1000 \times \left( \frac{(1 + 0.04)^6 - 1}{0.04} \right) \] Calculating \( (1 + 0.04)^6 \): \[ (1.04)^6 \approx 1.265319 \] Now substituting this back into the formula: \[ FV = 1000 \times \left( \frac{1.265319 - 1}{0.04} \right) \] Calculating the fraction: \[ \frac{1.265319 - 1}{0.04} = \frac{0.265319}{0.04} \approx 6.632975 \] Now calculating the future value: \[ FV \approx 1000 \times 6.632975 \approx 6632.98 \] ### Step 3: Adjust for annuity due Since this is an annuity due, we need to multiply the future value of the ordinary annuity by \( (1 + r) \) to account for the extra period of interest: \[ FV_{\text{due}} = FV \times (1 + r) \] Substituting the values: \[ FV_{\text{due}} = 6632.98 \times (1 + 0.04) = 6632.98 \times 1.04 \approx 6905.90 \] ### Final Result The future value of the annuity due at the end of the 3-year period is approximately: \[ \boxed{6905.90} \]