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!