How much do you  need   in your  account today  if you expect to  make quarterly withdrawals of $10,900 for 11 years and also make a special withdrawal of $22,400 in 11 years. The expected return for the account is 3.17 percent per quarter and the first regular withdrawal will be made today. 

$______ Round your answer to the nearest dollar 

This is a financial problem involving the present value of an annuity and a lump-sum withdrawal. We'll break it down into two parts:

1. **The Present Value of the Quarterly Withdrawals**: 
   Since the first withdrawal is made today, it is an *annuity due*. The present value (PV) of an annuity due can be calculated using the following formula:

\[
PV_{\text{annuity}} = P \times \left(1 + r\right) \times \left(1 - (1 + r)^{-n}\right) \div r
\]
where:
- $P = 10,900$ (the quarterly withdrawal)
- $r = 3.17\% = 0.0317$ (the interest rate per quarter)
- $n = 11 \times 4 = 44$ quarters (since withdrawals are over 11 years)

2. **The Present Value of the Lump-Sum Withdrawal**: 
   The special withdrawal of $22,400 is made after 44 quarters. We calculate its present value using the formula for a lump-sum present value:

\[
PV_{\text{lump sum}} = \frac{F}{(1 + r)^n}
\]
where:
- $F = 22,400$ (the lump-sum withdrawal)
- $r = 0.0317$
- $n = 44$

Let me now calculate the total amount you'd need today.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like to try calculating it manually or use another tool, here's a brief summary of the process:
1. Calculate the present value of the quarterly withdrawals using the annuity due formula.
2. Compute the present value of the lump-sum withdrawal after 11 years.
3. Add both present values together to get the total amount needed today.

Would you like more details on the steps, or help with another calculation?

Here are 5 related questions you might explore:
1. How is the present value of an annuity due different from an ordinary annuity?
2. What happens if the interest rate changes to a different value?
3. How would the calculation change if the withdrawals were monthly instead of quarterly?
4. What if the lump-sum withdrawal occurred earlier, say in 5 years?
5. How does compound interest affect these types of problems?

**Tip:** When calculating present values, always ensure you're using the correct time period and interest rate for consistency!

How much do you need in your account today if you expect to make quarterly withdrawals of $10,900 for 11 years and also make a special withdrawal of $22,400 in 11 years. The expected return for the account is 3.17 percent per quarter and the first regular withdrawal will be made today. $______ Round your answer to the nearest dollar.

Learn how to calculate the present value of quarterly withdrawals of $10,900 for 11 years with an interest rate of 3.17% per quarter, plus a special lump-sum withdrawal of $22,400 in the 11th year. Step-by-step guide to using annuity due and lump-sum present value formulas. Suitable for finance students and advanced high school math.

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