Final answer:
The present and future values of an annuity require calculating the value of each payment in today's terms and the compounded value at the term's end. These values are then summed to obtain the annuity's total present and future values, using financial mathematics formulas and the effective semiannual interest rate.
Step-by-step explanation:
The student's question regarding the calculation of present and future values of an annuity requires the application of financial mathematics principles. Firstly, we must find the present value (PV) of the annuity. Since the payments are semiannual, there are 7 payments in total (3.5 years x 2). Using the formula for the present value of an ordinary annuity and a nominal annual interest rate of 4% compounded monthly (which translates to an effective semiannual rate), we calculate the PV of each semiannual payment of $2750. Then, summing them up gives us the total PV of the annuity.To find the future value (FV) of the annuity, we compound the payments at the same effective semiannual interest rate until the end of the annuity term. We add up all these compounded values to find the total FV. Without sufficient information to do the exact calculations here, we cannot confidently provide the correct main answer from the options given A, B, C, or D.In a conclusion, the calculation of both the present and future values involves determining the worth of each payment at the respective points in time and summing them to get the total value for the annuity.