This problem can be solved using the concept of the present value of an annuity, as you want to withdraw a fixed amount annually for a fixed period, with an account that earns interest.

Given:

• Annual withdrawal amount, $PMT = 50,000$
• Number of years, $n = 15$
• Interest rate, $r = 7\% = 0.07$

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

The present value of an annuity formula is: $PV = PMT \times \frac{1 - (1 + r)^{-n}}{r}$

Substituting the values:

$PV = 50,000 \times \frac{1 - (1 + 0.07)^{-15}}{0.07}$

Let's calculate this value.

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

Total withdrawals: $\text{Total Withdrawals} = PMT \times n = 50,000 \times 15$

c) How much of that money is interest?

To find the total interest, subtract the initial amount (from part a) from the total amount withdrawn:

$\text{Interest} = \text{Total Withdrawals} - PV$

I'll calculate these values now.Here are the results:

a) You need approximately $455,395.70 in your account at the beginning.

b) The total amount you will pull out of the account over 15 years is $750,000.

c) Of that money, $294,604.30 is interest earned.

Would you like more details on the calculations, or do you have any questions?

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Here are some related questions to explore this concept further:

1. How would changing the interest rate to 5% affect the initial amount needed?
2. What if the withdrawal period was 20 years instead of 15—how would that change the required initial amount?
3. If withdrawals were $60,000 annually, how would the necessary initial amount change?
4. How does the present value calculation differ for monthly withdrawals instead of annual ones?
5. What is the impact of inflation on the purchasing power of $50,000 over 15 years?

Tip: When calculating the present value of an annuity, changing the interest rate or number of periods significantly impacts the initial amount needed.