This problem involves determining the present value (PV) of a series of quarterly withdrawals, including one special withdrawal at the end of 2 years. The method used is called the "present value of annuity" formula and the "present value of a lump sum" formula.

Key Data:

• Quarterly withdrawals: $2,000
• Special withdrawal at the end of 2 years: $7,500
• Interest rate per quarter: 2.05% = 0.0205
• Number of quarters: 2 years × 4 quarters/year = 8 quarters
• First withdrawal: After 3 months (1st quarter)

Steps:

1. Present Value of Regular Quarterly Withdrawals (Annuity): The formula for the present value of an ordinary annuity (withdrawals happen at the end of each period) is:

   $PV_{\text{annuity}} = W \times \frac{1 - (1 + r)^{-n}}{r}$

   Where:

   • $W$ is the regular withdrawal amount ($2,000),
   • $r$ is the quarterly interest rate (0.0205),
   • $n$ is the total number of periods (8 quarters).

2. Present Value of the Special Withdrawal (Lump Sum): The present value of the special withdrawal at the end of 2 years (8th quarter) is:

   $PV_{\text{lump sum}} = F \times \frac{1}{(1 + r)^n}$

   Where:

   • $F$ is the lump sum withdrawal ($7,500),
   • $r$ is the quarterly interest rate (0.0205),
   • $n$ is the number of periods (8 quarters).

Now let's calculate this.You would need approximately $20,995.57 in your account today to cover the quarterly withdrawals of $2,000 for 2 years and the special withdrawal of $7,500 at the end of 2 years, given an expected quarterly return of 2.05%.

Would you like more details on the calculations, or have any questions?

Here are some related questions to consider:

1. How does the interest rate affect the present value?
2. What if the withdrawals were made monthly instead of quarterly?
3. How would increasing the number of quarters (e.g., 3 years instead of 2) impact the required present value?
4. What happens if the special withdrawal occurs earlier, say after 1 year?
5. How would the results change if the account earns a higher return per quarter?

Tip: When planning withdrawals, it's important to account for both the timing of withdrawals and the interest rate, as they significantly affect the amount you need to start with.