How much do you need in your account today if you expect to make quarterly withdrawals of $8,600 for 12 years and also make a special withdrawal of $20,300 in 12 years. The expected return for the account is 3.50 percent per quarter and the first regular withdrawal will be made today.


This problem is asking for the present value of a series of withdrawals that will occur in the future, given a specific interest rate and timing for each withdrawal. We need to calculate the present value (PV) of both the regular quarterly withdrawals and the special withdrawal that occurs at the end of 12 years.

### Given:
- Quarterly withdrawal = $8,600
- Time period for withdrawals = 12 years = $ 12 \times 4 = 48 $ quarters
- Special withdrawal at the end of 12 years = $20,300
- Interest rate per quarter = 3.50% or 0.035
- First withdrawal is today (this is an annuity due)

### Steps to solve:

1. **Present value of the quarterly withdrawals:**
   Since the first withdrawal happens today, this is an *annuity due*. We will use the present value formula for an annuity due:

   \[
   PV_{\text{withdrawals}} = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \times (1 + r)
   \]

   Where:
   - $ C $ = $8,600 (quarterly withdrawal)
   - $ r $ = 0.035 (quarterly interest rate)
   - $ n $ = 48 (total number of quarters)

2. **Present value of the special withdrawal:**
   The $20,300 special withdrawal occurs at the end of 12 years, so we discount it back to the present using the following formula:

   \[
   PV_{\text{special}} = \frac{F}{(1 + r)^n}
   \]

   Where:
   - $ F $ = $20,300
   - $ r $ = 0.035
   - $ n $ = 48

3. **Total present value (amount required today):**
   The total amount you need in your account today will be the sum of the present value of the regular quarterly withdrawals and the special withdrawal.

Let me calculate this for you.The total amount you need in your account today is approximately **$209,428.84** in order to make quarterly withdrawals of $8,600 for 12 years, along with the special withdrawal of $20,300 at the end of 12 years, assuming a quarterly interest rate of 3.50% and that the first withdrawal is made today.

Do you want more details or have any questions?

Here are 5 related questions:
1. How would the result change if the interest rate were compounded monthly instead of quarterly?
2. What if the special withdrawal amount was different? How would that affect the total amount needed today?
3. How much would you need if the withdrawals occurred at the end of each quarter instead of the beginning?
4. What would be the future value of the account if no withdrawals were made?
5. How does the duration (12 years) affect the amount you need today?

**Tip:** Always consider whether payments occur at the beginning (annuity due) or end (ordinary annuity) of periods, as this changes the present value calculation.

How much do you need in your account today if you expect to make quarterly withdrawals of $8,600 for 12 years and also make a special withdrawal of $20,300 in 12 years. The expected return for the account is 3.50 percent per quarter and the first regular withdrawal will be made today.

Find out how to calculate the present value of quarterly withdrawals of $8,600 for 12 years with a special withdrawal of $20,300 at the end of 12 years. This guide uses the concept of annuity due and the present value formula to determine how much you need in your account today, assuming a quarterly interest rate of 3.50%.

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