Questions: Find the future value of the annuity due. Round to the nearest cent. Find the future value of an annuity due of 7500 made at the beginning of each semiannual period for 6 years at 8% compounded semiannually.

Solution Steps

We are given the following parameters for the annuity due:

• Payment per period, \( P = 7500 \)
• Annual interest rate, \( 8\% \), which translates to a semiannual interest rate of \( r = \frac{8\%}{2} = 4\% = 0.04 \)
• Total number of periods over 6 years with semiannual payments, \( n = 6 \times 2 = 12 \)

The future value of an annuity due is calculated using the formula: \[ FV_{\text{due}} = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \times (1 + r) \] Substituting the identified parameters into the formula: \[ FV_{\text{due}} = 7500 \times \left( \frac{(1 + 0.04)^{12} - 1}{0.04} \right) \times (1 + 0.04) \]

After performing the calculations, we find: \[ FV_{\text{due}} \approx 117201.2826206979 \] Rounding this to the nearest cent gives: \[ FV_{\text{due}} \approx 117201.28 \]

Final Answer