You plan to save $36,640 per year for 4 years, with your first savings contribution in 1 year. You then plan to withdraw $X per year for 5 years, with your first withdrawal expected in 4 years. What is X if the expected return per year is 17.02 percent per year?



Let's break this problem down in stages. First, you are saving for 4 years, then withdrawing for 5 years, and the return on your investment is 17.02% per year.

### Step 1: Saving for 4 years
You are saving $36,640 per year for 4 years, with a return of 17.02% per year. The first deposit occurs in 1 year, the second in 2 years, and so on. This means we can treat this as a future value of an annuity problem.

The formula for the future value of an annuity is:

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

Where:
- $ FV $ is the future value of the savings,
- $ P $ is the annual payment (in this case, $36,640),
- $ r $ is the interest rate per period (17.02% = 0.1702),
- $ n $ is the number of periods (4 years).

Let’s calculate the future value of the savings:

\[
FV = 36,640 \times \frac{(1 + 0.1702)^4 - 1}{0.1702}
\]

### Step 2: Withdrawals for 5 years
After 4 years, you plan to withdraw an amount $ X $ for 5 years, starting at the end of the 4th year. The future value calculated above will now serve as the present value for this series of withdrawals. Since the interest rate remains at 17.02%, we will calculate the amount $ X $ using the present value of an annuity formula:

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

Where:
- $ PV $ is the present value (the amount accumulated after 4 years),
- $ X $ is the annual withdrawal,
- $ r $ is the interest rate per period (0.1702),
- $ n $ is the number of withdrawals (5 years).

Let me calculate both parts for you.The future value of your savings after 4 years will be approximately **$188,403**.

The annual withdrawal amount $ X $ that you can withdraw for 5 years, starting at the end of the 4th year, will be approximately **$58,915.03**.

Would you like more details or have any questions about the calculations?

Here are 5 related questions to expand on this topic:
1. How would the withdrawal amount change if the interest rate were different?
2. What if you want to start withdrawing immediately after the savings period ends?
3. How would inflation affect the real value of your withdrawals?
4. What happens if you skip one year of savings or make an extra contribution?
5. How does the length of the withdrawal period impact the annual withdrawal amount?

**Tip:** The higher the interest rate, the larger the future value of your savings, but also the larger the impact of compounding during the withdrawal period!

You plan to save $36,640 per year for 4 years, with your first savings contribution in 1 year. You then plan to withdraw $X per year for 5 years, with your first withdrawal expected in 4 years. What is X if the expected return per year is 17.02 percent per year?

Discover how to calculate annual withdrawals based on saving $36,640 per year for 4 years at a 17.02% annual return. Learn how to apply future value and present value of annuity formulas to determine the amount you can withdraw annually over 5 years. Perfect for students and professionals learning finance concepts.

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