How much do you need in your account today if you expect to make quarterly withdrawals of $2,000 for 2 years and also make a special withdrawal of $7,500 in 2 years. The expected return for the account is 2.05 percent per quarter and the first regular withdrawal will be made in 3 months. 

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.

How much do you need in your account today if you expect to make quarterly withdrawals of $2,000 for 2 years and also make a special withdrawal of $7,500 in 2 years? The expected return for the account is 2.05 percent per quarter, and the first regular withdrawal will be made in 3 months.

Calculate the present value needed in your account today to make quarterly withdrawals of $2,000 over 2 years, with an additional special withdrawal of $7,500 at the end. Learn how the present value of an annuity and a lump sum are used to determine the amount you need, considering an interest rate of 2.05% per quarter.

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