





You said:
Now let's look at things a little differently. Suppose that once you retire, you want to be able to withdraw $73,200 per year (starting one year from your retirement) for a total of 25 years during your retirement. How much would you need in your account when you retire to make this work assuming an annual interest rate of 4.5%? Hints: This is the PV of a regular annuity and remember that with this type of problem, you are withdrawing a set amount every year and at the end of the 25 years, your account balance is zero. 

To solve this problem, we need to find the present value (PV) of a regular annuity. This represents the amount you need in your account at the time of retirement to withdraw a fixed amount of $73,200 annually for 25 years, assuming an interest rate of 4.5% per year.

### Formula for Present Value of an Annuity

The formula for the present value of a regular annuity is:

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

where:
- $ P $ is the annual withdrawal amount ($73,200),
- $ r $ is the annual interest rate (4.5% or 0.045),
- $ n $ is the total number of years (25 years).

### Step-by-Step Calculation

1. **Convert the interest rate to a decimal**:  
   $ r = 4.5\% = 0.045 $.

2. **Substitute the values into the formula**:

\[
PV = 73200 \times \left( \frac{1 - (1 + 0.045)^{-25}}{0.045} \right)
\]

Now, let's calculate the present value using this formula.The amount you would need in your account at the time of retirement to be able to withdraw $73,200 annually for 25 years, assuming an annual interest rate of 4.5%, is **$1,085,424.90**.

Would you like more details or have any other questions? 

Here are some related questions you might find helpful:
1. How does the present value change if the interest rate increases to 5%?
2. What is the future value of these withdrawals if the interest rate is 4.5%?
3. How does the withdrawal amount change if you plan to withdraw over 30 years instead of 25?
4. What if you want to make monthly withdrawals instead of annual?
5. How can you calculate the interest rate needed to withdraw $80,000 annually for 25 years?

**Tip:** The present value formula is useful for calculating how much money you need now to meet future financial goals!

Now let's look at things a little differently. Suppose that once you retire, you want to be able to withdraw $73,200 per year (starting one year from your retirement) for a total of 25 years during your retirement. How much would you need in your account when you retire to make this work assuming an annual interest rate of 4.5%? Hints: This is the PV of a regular annuity and remember that with this type of problem, you are withdrawing a set amount every year and at the end of the 25 years, your account balance is zero.

Learn how to calculate the present value of an annuity for $73,200 annual withdrawals over 25 years at a 4.5% interest rate. This problem involves key concepts like the present value of an annuity, financial mathematics, and the time value of money. Suitable for college students or anyone learning financial planning.

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