Sharon has worked for a company with a retirement program, and today is retiring from her job with the amount of $157000 in her retirement account. She decides to withdrawal an equal amount from this account, once a year, beginning immediately, and ending 22 years from today (for a total of 23 payments). If the interest rate is 5.75%, solve for the annuity amount such that she uses up her full accumulation.

To solve this problem, we need to determine the amount of each annual withdrawal from Sharon's retirement account, given that she will make 23 equal withdrawals, starting immediately, and the interest rate is 5.75%. This is an annuity problem where the annuity payments are made at the beginning of each period (annuity due).

### Key Parameters:
- Present value $ PV = 157,000 $
- Number of payments $ n = 23 $
- Interest rate per period $ r = 5.75\% = 0.0575 $
- Payments start immediately, so it's an **annuity due**.

#### Formula for Annuity Due:
The formula to calculate the payment $ P $ for an annuity due is:

\[
PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \times (1 + r)
\]

Where:
- $ PV $ is the present value of the annuity (total retirement amount),
- $ P $ is the annuity payment (amount withdrawn each year),
- $ r $ is the interest rate per period (here, 5.75% or 0.0575),
- $ n $ is the number of payments (23 years).

Now, let's solve for $ P $. I'll calculate it.The annual withdrawal amount Sharon should take is approximately **$11,797.60**. This ensures that after 23 payments, starting immediately, her retirement account will be fully used up, given the 5.75% interest rate.

Would you like more details or have any questions?

Here are some related questions for deeper understanding:
1. How does the interest rate affect the annuity payment?
2. What is the difference between an annuity due and an ordinary annuity?
3. How would the solution change if the withdrawals were monthly instead of yearly?
4. What if Sharon lives longer and needs to make more withdrawals—how would that affect her payments?
5. How would the final amount change if she started her withdrawals one year later?

**Tip**: In an annuity due, payments start immediately, which slightly increases the value of each payment compared to an ordinary annuity.

Sharon has worked for a company with a retirement program, and today is retiring from her job with the amount of $157000 in her retirement account. She decides to withdraw an equal amount from this account, once a year, beginning immediately, and ending 22 years from today (for a total of 23 payments). If the interest rate is 5.75%, solve for the annuity amount such that she uses up her full accumulation.

Calculate the annual withdrawal amount for Sharon's retirement fund of $157,000, using the annuity due formula. With an interest rate of 5.75%, this detailed solution ensures 23 equal withdrawals starting immediately, solving for the exact payment amount using financial mathematics.

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