You want to be able to withdraw $20,000 each year for 15 years. Your account earns 8% 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This problem involves calculating the present value of an annuity, the total amount withdrawn, and the total interest earned. Let's solve it step-by-step.

---

### (a) How much do you need in your account at the beginning?
The present value of an annuity formula is used here:

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

Where:
- $ P = 20,000 $ (annual withdrawal)
- $ r = 0.08 $ (annual interest rate)
- $ n = 15 $ (number of years)

\[
PV = 20,000 \times \frac{1 - (1 + 0.08)^{-15}}{0.08}
\]

Let me calculate this.

---

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

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

---

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

\[
\text{Interest} = \text{Total withdrawals} - PV
\]

Let me compute all values for you.# Given data
P = 20000  # annual withdrawal
r = 0.08  # annual interest rate
n = 15  # number of years

# (a) Present Value calculation
PV = P * ((1 - (1 + r)**-n) / r)

# (b) Total money withdrawn
total_withdrawals = P * n

# (c) Total interest
interest = total_withdrawals - PV

PV, total_withdrawals, interest(171189.57375852752, 300000, 128810.42624147248)(171189.57375852752, 300000, 128810.42624147248)success### Results:

**(a)** You need **$171,189.57** in your account at the beginning.  
**(b)** The total amount of money you will pull out of the account is **$300,000**.  
**(c)** The total interest earned on your account is **$128,810.43**.

---

### Would you like more details or have further questions?  
Here are 5 related questions for exploration:  
1. How would the required initial balance change with a different interest rate?  
2. What if the withdrawals were made monthly instead of yearly?  
3. How does the account balance decline over time during the withdrawal period?  
4. How can inflation affect the value of these withdrawals?  
5. How to calculate future value instead of present value for such an annuity?

**Tip:** Always ensure the interest rate and compounding period match the frequency of withdrawals for accurate calculations!

You want to be able to withdraw $20,000 each year for 15 years. Your account earns 8% 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?

Discover how to calculate the present value required for annual withdrawals of $20,000 over 15 years with an 8% interest rate. Learn step-by-step calculations, including total withdrawals and interest earned. Suitable for high school and college-level finance studies.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation