You plan to retire in 8 years with $X. You plan to withdraw $147,200 per year for 17 years. The expected return is 17.92 percent per year and the first regular withdrawal is expected in 8 years. What is X? Round to the nearest dollar for your answer.

This problem can be approached in two main parts:

1. **Determine the present value of withdrawals**: Since you are withdrawing $147,200 annually for 17 years, starting in 8 years, we need to discount this series of withdrawals back to the time you retire (in 8 years) to find the amount needed at retirement. This requires using the present value of an annuity formula.

2. **Discount that amount further to today’s value (which is X)**: After determining how much you'll need at retirement, we'll discount that value back to today to determine $ X $, the amount you need to save today.

### Step-by-Step Breakdown:

#### Step 1: Present Value of Withdrawals at Retirement
The formula for the present value of an annuity is:
\[
PV_{\text{annuity}} = \frac{P \times \left[1 - (1 + r)^{-n}\right]}{r}
\]
Where:
- $ P = 147,200 $ (annual withdrawal),
- $ r = 0.1792 $ (annual return rate),
- $ n = 17 $ (number of withdrawals).

#### Step 2: Discount this to today
Once we have the present value of the withdrawals at the time of retirement, we need to discount this back to today’s value using the formula:
\[
PV = \frac{FV}{(1 + r)^t}
\]
Where:
- $ t = 8 $ (time to retirement).

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Learn how to calculate the required retirement savings (X) with an expected annual return of 17.92% and annual withdrawals of $147,200 over 17 years. This problem applies concepts like the time value of money, annuities, and discounting cash flows. Suitable for advanced high school and college students.

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