You want to be able to withdraw $20,000 from your account each year for 15 years after you retire.

You expect to retire in 30 years.

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

$

Round your answer to the nearest cent.

To solve this problem, we'll use two main steps. First, we'll determine how much money you will need at the time of retirement to withdraw $20,000 annually for 15 years. Then, we'll calculate how much you need to deposit each year to accumulate that sum over 30 years.

### Step 1: Determine how much money is needed at retirement

To calculate the lump sum required at retirement to withdraw $20,000 annually for 15 years, we'll use the present value of an annuity formula:

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

Where:
- $ P = 20,000 $ (the annual withdrawal)
- $ r = 9\% = 0.09 $ (the interest rate per period)
- $ n = 15 $ (the number of years of withdrawals)

Substitute the values:

\[
PV = 20,000 \times \left( 1 - \frac{1}{(1 + 0.09)^{15}} \right) \div 0.09
\]

\[
PV = 20,000 \times \left( 1 - \frac{1}{(1.09)^{15}} \right) \div 0.09
\]

\[
PV = 20,000 \times \left( 1 - \frac{1}{3.6424} \right) \div 0.09
\]

\[
PV = 20,000 \times \left( 1 - 0.2746 \right) \div 0.09
\]

\[
PV = 20,000 \times 0.7254 \div 0.09
\]

\[
PV = 14508 \div 0.09
\]

\[
PV = 161,200
\]

So, you will need $161,200 at the time of retirement to make the withdrawals.

### Step 2: Calculate the annual deposit required

Now, we need to determine how much to deposit each year to accumulate $161,200 in 30 years. We'll use the future value of an annuity formula:

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

Where:
- $ FV = 161,200 $ (the amount you need at retirement)
- $ r = 9\% = 0.09 $ (the interest rate per period)
- $ n = 30 $ (the number of years until retirement)

Rearranging the formula to solve for $ P $:

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

Substitute the values:

\[
P = \frac{161,200 \times 0.09}{(1 + 0.09)^{30} - 1}
\]

\[
P = \frac{161,200 \times 0.09}{(1.09)^{30} - 1}
\]

\[
P = \frac{14,508}{13.2677 - 1}
\]

\[
P = \frac{14,508}{12.2677}
\]

\[
P = 1,182.32
\]

### Final Answer:
You will need to deposit **$1,182.32** per year to achieve your retirement goals.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does changing the interest rate affect the annual deposit required?
2. What if the withdrawal period were 20 years instead of 15?
3. How much would the required deposit be if you planned to save for only 20 years before retirement?
4. How would a lower interest rate, like 7%, change the calculation?
5. What if you want to increase your annual withdrawals to $25,000?

**Tip:** When planning for retirement, always account for inflation and tax implications, as they can affect your real savings needs!

You want to be able to withdraw $20,000 from your account each year for 15 years after you retire. You expect to retire in 30 years. If your account earns 9% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?

Calculate how much you need to deposit each year to withdraw $20,000 annually for 15 years after retirement. This finance problem involves the Present Value of an Annuity and Future Value of an Annuity formulas with a 9% interest rate. Learn how to achieve your retirement goals with detailed step-by-step solutions.

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