You want to be able to withdraw $20,000 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?

$

This is a problem involving the calculation of the present value of an annuity, which is a series of equal annual withdrawals from an account earning interest. Let's go step by step.

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

To calculate the amount needed at the beginning, we use the formula for the **present value of an annuity**:

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

Where:
- $ PV $ is the present value (the amount needed in the account at the beginning).
- $ P $ is the annual withdrawal ($20,000).
- $ r $ is the interest rate per period (7% or 0.07).
- $ n $ is the number of periods (15 years).

Substitute the values:

\[
PV = 20000 \times \left( \frac{1 - (1 + 0.07)^{-15}}{0.07} \right)
\]

Let me calculate this for you.

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

You are withdrawing $20,000 per year for 15 years, so the total amount withdrawn is:

\[
\text{Total withdrawals} = 20,000 \times 15 = 300,000
\]

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

To find the total interest, subtract the initial amount from the total amount withdrawn:

\[
\text{Interest} = \text{Total withdrawals} - \text{Initial amount (PV)}
\]

Let me calculate both the initial amount and the interest.### a) How much do you need in your account at the beginning?
You need **$182,158.28** in your account at the beginning.

### b) How much total money will you pull out of the account?
You will withdraw a total of **$300,000** over 15 years.

### c) How much of that money is interest?
Out of the total withdrawn, **$117,841.72** is from interest earned on the account.

Do you want further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the required initial amount change if the interest rate was higher?
2. What would happen if you increased the withdrawal amount each year by a certain percentage?
3. How would the present value change if the withdrawal period was shorter, say 10 years?
4. What happens if you withdraw the money quarterly instead of annually?
5. How can you calculate the future value of these withdrawals?

**Tip:** When withdrawing funds from an interest-bearing account, always check how the interest compounds (e.g., yearly, quarterly) as it significantly affects the calculations.

You want to be able to withdraw $20,000 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 needed to withdraw $20,000 annually for 15 years from an account earning 7% interest. This problem uses the present value of an annuity formula to solve for the starting balance, total withdrawals, and interest earned. Perfect for high school students in Grades 10-12.

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