You expect to live for thirty years after retiring. If your retirement account earns 3.5% and you want it to provide your annual living expenses of $100,000, paid to you at the end of each year, how much will you have to have in that account when you retire?

(Round your answer to the nearest dollar.

To determine how much you need in your retirement account when you retire, we can use the present value of an annuity formula. The formula is:

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

Where:
- $PV$ is the present value (the amount needed at retirement),
- $PMT$ is the annual payment ($100,000),
- $r$ is the interest rate (3.5% or 0.035),
- $n$ is the number of years (30 years).

Let's plug in the values and calculate:

\[
PV = \frac{100,000}{0.035} \times \left(1 - \frac{1}{(1 + 0.035)^{30}}\right)
\]

I'll calculate this for you.You will need approximately **$1,839,205** in your retirement account when you retire to ensure it provides $100,000 annually for 30 years, with a 3.5% interest rate.

Would you like more details on the calculation or have any other questions?

Here are some related questions you might find useful:
1. How does the present value of an annuity formula change if payments are made at the beginning of each period?
2. What happens to the required retirement amount if the interest rate is higher?
3. How would inflation affect the amount you need to save for retirement?
4. What if you want to withdraw a different amount each year?
5. How would a one-time withdrawal early in retirement affect the remaining balance?
6. What if your retirement account has a different interest rate each year?
7. How can you calculate the future value of your current retirement savings?
8. What other factors should you consider when planning for retirement?

**Tip:** When planning for retirement, it's crucial to factor in inflation, as it can significantly impact your purchasing power over time.

Learn how to calculate the amount needed in your retirement account using the Present Value of Annuity formula. This problem involves determining the present value required to provide $100,000 annually for 30 years at a 3.5% interest rate. Essential for retirement planning.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation