You want to be able to withdraw $35,000 from your account each year for 30 years after you retire.

You expect to retire in 15 years.

If your account earns 9% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?

To solve this problem, we can break it down into two main parts:

1. Determine the amount needed at the time of retirement to be able to withdraw $35,000 each year for 30 years.
2. Calculate the annual deposit required for the next 15 years to accumulate the amount determined in the first step.

### Step 1: Calculate the required retirement fund
To determine the amount needed at retirement, we use the present value of an annuity formula since you will be making regular withdrawals:

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

where:
- $ PV $ is the present value (the amount needed at retirement).
- $ PMT $ is the annual withdrawal amount (\$35,000).
- $ r $ is the annual interest rate (9% or 0.09).
- $ n $ is the number of years of withdrawals (30 years).

\[ PV = 35000 \times \left(1 - (1 + 0.09)^{-30}\right) / 0.09 \]

Calculating the above expression:

\[ PV = 35000 \times \left(1 - (1 + 0.09)^{-30}\right) / 0.09 \]
\[ PV = 35000 \times \left(1 - (1.09)^{-30}\right) / 0.09 \]
\[ PV = 35000 \times \left(1 - 0.068301\right) / 0.09 \]
\[ PV = 35000 \times 0.931699 / 0.09 \]
\[ PV = 35000 \times 10.3522 \]
\[ PV = 362,327 \]

So, you will need $362,327 at the time of retirement.

### Step 2: Calculate the annual deposit required
To accumulate $362,327 in 15 years with an annual interest rate of 9%, we use the future value of an annuity formula:

\[ FV = PMT \times \left((1 + r)^n - 1\right) / r \]

We need to solve for $ PMT $:

\[ 362327 = PMT \times \left((1 + 0.09)^{15} - 1\right) / 0.09 \]

Rearranging to solve for $ PMT $:

\[ PMT = 362327 \times 0.09 / \left((1 + 0.09)^{15} - 1\right) \]
\[ PMT = 362327 \times 0.09 / \left(3.6425 - 1\right) \]
\[ PMT = 362327 \times 0.09 / 2.6425 \]
\[ PMT = 362327 \times 0.03406 \]
\[ PMT = 12,340 \]

So, you will need to deposit approximately $12,340 each year for the next 15 years to achieve your retirement goal.

Would you like more details or have any questions?

Here are 5 questions you might consider asking next:
1. How does compound interest affect long-term savings plans?
2. What are other investment options to achieve similar retirement goals?
3. How does changing the interest rate impact the annual deposit amount?
4. What if you want to withdraw a different amount each year in retirement?
5. How would inflation affect your retirement withdrawals?

**Tip:** Always review your retirement plan regularly to ensure it aligns with your financial goals and market conditions.

Learn how to plan your retirement savings by calculating the annual deposit required to achieve $35,000 annual withdrawals for 30 years, starting 15 years from now. Detailed step-by-step solution using compound interest formulas.

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