You want to be able to withdraw $50,000 each year for 15 years. Your account earns 7% interest. a) How much do you need in your account at the beginning? 2 b) How much total money will you pull out of the account? c) How much of that money is interest?

This problem involves determining the present value of an annuity, which is the amount you need to deposit initially to withdraw $50,000 per year for 15 years with a 7% annual interest rate.

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

To find how much you need at the beginning, we use the formula for the present value of an annuity:

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

Where:
- $ P = 50,000 $ (the annual withdrawal),
- $ r = 0.07 $ (the interest rate per year),
- $ n = 15 $ (the number of years).

Let's calculate this.

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

The total amount withdrawn will simply be the amount withdrawn each year multiplied by the number of years:

\[
\text{Total Withdrawn} = 50,000 \times 15
\]

### c) How much of that money is interest?

The total interest is the difference between the total amount withdrawn and the initial amount in the account (from part a). This is given by:

\[
\text{Interest} = \text{Total Withdrawn} - \text{Initial Deposit}
\]

Now, let's calculate each of these.### Results:

a) You need **$455,395.70** in your account at the beginning to be able to withdraw $50,000 each year for 15 years at a 7% interest rate.

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

c) Out of that, **$294,604.30** is interest earned over the 15 years.

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Would you like more details or have any other questions? Here are some related questions:

1. What would happen if the interest rate was lower or higher?
2. How does the duration (15 years) affect the required initial amount?
3. How much would you need if you wanted to withdraw for 20 years instead of 15?
4. What if you increased your annual withdrawal to $60,000?
5. How does compound interest affect the amount of interest earned?

**Tip:** The longer the withdrawal period, the more interest you accumulate, reducing the initial deposit needed.

You want to be able to withdraw $50,000 each year for 15 years. Your account earns 7% interest. a) How much do you need in your account at the beginning? b) How much total money will you pull out of the account? c) How much of that money is interest?

Learn how to calculate the initial amount required to withdraw $50,000 annually for 15 years at a 7% interest rate. This problem covers key financial math concepts like the present value of annuities and total interest earned. Find out how much you need to start with and how much total interest you earn.

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