your uncle has $310,000 invested at 7.3%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, starting at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

To solve this, we need to determine how many years your uncle can withdraw $35,000 each year, given the initial investment, interest rate, and the desired final amount left ($25,000).

This is a type of **annuity problem** where we need to use the **Present Value of an Annuity formula**. The formula for the present value of an annuity (PVA) is:

\[
PVA = \frac{W}{r} \left( 1 - (1 + r)^{-n} \right)
\]

Where:
- $ PVA $ is the present value of the annuity, which in this case is $310,000 - 25,000 = 285,000 \) (since your uncle wants $25,000 left at the end).
- $ W $ is the annual withdrawal amount ($35,000).
- $ r $ is the interest rate per period (7.3%, or 0.073).
- $ n $ is the number of years (the value we are solving for).

We can rearrange this formula to solve for $ n $ (number of years). Let’s calculate it now.

\[
285,000 = \frac{35,000}{0.073} \left( 1 - (1 + 0.073)^{-n} \right)
\]

I’ll compute the value of $ n $.Your uncle can make withdrawals for approximately 12.81 years, which means he can make full withdrawals for 12 years and part of a year for the last withdrawal. 

If you'd like more details or a step-by-step breakdown, feel free to ask!

Here are some related questions you might be interested in:
1. How would the answer change if the interest rate was different?
2. What would happen if your uncle wanted to withdraw a different amount annually?
3. How does the interest rate affect the duration of withdrawals?
4. How can you calculate the amount left after each year of withdrawals?
5. What happens if your uncle wants more or less than $25,000 left at the end?

**Tip:** In annuity problems, increasing the withdrawal amount decreases the number of years the investment will last, while increasing the interest rate extends the duration.

Your uncle has $310,000 invested at 7.3%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, starting at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

Learn how to determine the duration of withdrawals from a retirement fund with an initial investment of $310,000 at a 7.3% interest rate. Calculate the number of years $35,000 can be withdrawn annually while leaving $25,000 at the end. This guide covers key concepts in annuities, present value, and the time value of money.

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