This problem is related to determining the present value of an annuity, where you withdraw a fixed amount every year, and the account earns a fixed interest rate.

(a) How much do you need in your account at the beginning?

The present value of an annuity formula is used for this calculation:

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

Where:

• $PV$ is the present value (amount needed at the beginning).
• $P = 45,000$ is the annual withdrawal.
• $r = 0.04$ is the interest rate per year.
• $n = 30$ is the number of years.

Now, let me calculate the initial amount you need.

(b) How much total money will you pull out of the account?

This is simply the annual withdrawal multiplied by the number of years:

$\text{Total withdrawals} = P \times n = 45,000 \times 30$

(c) How much of that money is interest?

The interest can be found by subtracting the initial amount (calculated in part (a)) from the total amount withdrawn over 30 years.

$\text{Interest} = \text{Total withdrawals} - \text{Initial amount}$

Let me calculate these values for you.### Answers:

(a) You need $778,141.50 in your account at the beginning.

(b) The total amount you will pull out of the account over 30 years is $1,350,000.

(c) The total interest earned over that period is $571,858.50.

Would you like further details or clarification on any part of this solution?

Here are 5 related questions you might find interesting:

1. How does changing the interest rate affect the initial amount needed?
2. What if you want to withdraw $45,000 for 40 years instead of 30?
3. What would happen if the account earned 3% interest instead of 4%?
4. How does the withdrawal frequency (monthly vs yearly) affect the total interest?
5. How much more would you need initially if you plan to withdraw $50,000 annually?

Tip: Using the annuity formula helps plan for long-term withdrawals effectively, ensuring you don't run out of funds too soon!